Once you've done that, refresh this page to start using Wolfram|Alpha. WolframAlpha computational knowledge AI. Graph f(x)=ln(x)ln(x) function graph. Natural logarithm graph. y = f (x) = ln(x) ln(x) graph properties. ln(x) is defined for positive values of x. ln(x) is not defined for real non positive values of x. ln(x)<0 for 0<x<1; ln(x)=0 for x=1; ln(x)>0 for x>1; ln(x) rulesĐồ thị của ln (x) đồ thị hàm số ln (x). Đồ thị lôgarit tự nhiên. y = f ( x) = ln ( x) Thuộc tính đồ thị ln (x) ln (x) được xác định cho các giá trị dương của x. ln (x) không được xác định cho các giá trị thực không dương của x. ln (x) <0 với 0 <x <1; ln (x) = 0 cho x = 1; ln ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.This topic covers: - Radicals & rational exponents - Graphs & end behavior of exponential functions - Manipulating exponential expressions using exponent properties - Exponential growth & decay - Modeling with exponential functions - Solving exponential equations - Logarithm properties - Solving logarithmic equations - Graphing logarithmic functions - Logarithmic scale So when you see ln(x), just remember it is the logarithmic function with base e: log e (x). Graph of f(x) = ln(x) At the point (e,1) the slope of the line is 1/e and the line is tangent to the curve. Naturlig logaritm (ln) definition; Naturliga logaritm (ln) regler och egenskaper. Derivat av naturlig logaritm (ln) Integral av naturlig logaritm (ln) Komplex logaritm; Graf för ln (x) Naturliga logaritmer (ln) tabell; Naturlig logaritmräknare; Definition av naturlig logaritm. När. e y = x. Då är bas e-logaritmen för x. ln ( x) = log e ... ln(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…Graph Logarithmic Functions. To graph a logarithmic function y = log a x, y = log a x, it is easiest to convert the equation to its exponential form, x = a y. x = a y. Generally, when we look for ordered pairs for the graph of a function, we usually choose an x-value and then determine its corresponding y-value. This means the graph of y = ln(x) where x is a negative real number, really consists of countless parallel graphs also spaced at distances of 2π to each other.Yes if we know the function is a general logarithmic function. For example, look at the graph in the previous example. The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical asymptote. Review Properties of Logarithmic Functions. We first start with the properties of the graph of the basic logarithmic function of base a, f (x) = log a (x) , a > 0 and a not equal to 1. The domain of function f is the interval (0 , + ∞). The range of f is given by the interval (- ∞ , + ∞). Function f has a vertical asymptote given by the ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Are you looking to present your data in a visually appealing and easy-to-understand format? Look no further than creating a bar graph in Excel. A bar graph is a powerful tool for v...A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way. As opposed to a linear number line in which every unit of distance corresponds to adding by the same amount, on a logarithmic scale, every unit of length corresponds to multiplying the previous value by the same amount. The key difference between ln and log are given in the table below: Log. Ln. Log refers to a logarithm to the base 10. Ln refers to a logarithm to the base e. Log is also called a common logarithm. Ln is also called a natural logarithm. Common logarithm represented as log10(x) l o g 10 ( x)For problems that add/subtract to/from the x, simply solve for the exponent by using ln. In the example you gave: e^(x-4) = 2 x - 4 = ln(2) x = ln(2) + 4 An example for division: …For x > 0, y = ln(x) is equivalent to ey = x. We read ln(x) as, “the logarithm with base e of x ” or “the natural logarithm of x. The logarithm y is the exponent to which e must be raised to get x. Since the functions y = ex and y = ln(x) are inverse functions, ln(ex) = x for all x and e =ln ( x) x for x > 0.Before working with graphs, we will take a look at the domain (the set of input values) for which the logarithmic function is defined. Transformations of the parent function [latex]\,y= {\mathrm {log}}_ {b}\left (x\right)\, [/latex]behave similarly to those of other functions. Just as with other parent functions, we can apply the four types of ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Yes, if we know the function is a general logarithmic function. For example, look at the graph in Try It 11. The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical asymptote. It approaches from the right, so the domain is all points to the right, [latex]\left\{x|x>-3\right\}[/latex].Graph of [latex]y=log{_3}x[/latex]: The graph of the logarithmic function with base [latex]3[/latex] can be generated using the function’s inverse. Its shape is the same as other logarithmic functions, just with a different scale.Logarithmic Functions. The "basic" logarithmic function is the function, y = log b x, where x, b > 0 and b ≠ 1. The graph of the logarithmic function y = log x is shown. (Remember that when no base is shown, the base is …Given a logarithmic function with the form f(x) = logb(x + c), graph the translation. Identify the horizontal shift: If c > 0 ,shift the graph of f(x) = logb(x) left c units. If c < 0 ,shift the graph of f(x) = logb(x) right c units. Draw the vertical asymptote x = − c. Identify three key points from the parent function.Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... The logarithmic function graph passes through the point (1, 0), which is the inverse of (0, 1) for an exponential function. The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right if 0 < b < 1.To graph a log function: Always keep in mind that logs are inverses of exponentials; this will remind you of the shape you should expect the graph to have. Pick input values (that is, x -values) that are powers of the base; for instance, if the log's base is 5, then pick x -values like 52 and 5−1. List the corresponding y -values; for ...plot ln x. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Input interpretation. Plots. Real-valued plots. Download Page. POWERED BY THE WOLFRAM LANGUAGE. Related Queries: log(x) vs differentiate log(x) series log(x) volume of a general tetrahedron; plot 1/log(x)Using the online curve plotter. The online curve plotting software, also known as a graph plotter, is an online curve plotter that allows you to plot functions online. Simply enter the expression according to x of the function to be plotted using the usual mathematical operators. The curve plotter is particularly suitable for the function study ...Jul 13, 2022 · To get a feeling for how the base affects the shape of the graph, examine the graphs below. Notice that the larger the base, the slower the graph grows. For example, the common log graph, while it grows without bound, it does so very slowly. For example, to reach an output of 8, the input must be 100,000,000. The product rule: log b ( M N) = log b ( M) + log b ( N) This property says that the logarithm of a product is the sum of the logs of its factors. [Show me a numerical example of this property please.] We can use the product rule to rewrite logarithmic expressions.Plotting ln y against t produces a straight line; Note the second graph has ln y on the y-axis Log graphs have at least one logarithmic axis; Reading a value for ln y at t = 20 is easier than reading the value for y; Logarithmic axes are used where a wide range of numbers can occur it makes numbers smaller and easier to deal withFor problems that add/subtract to/from the x, simply solve for the exponent by using ln. In the example you gave: e^(x-4) = 2 x - 4 = ln(2) x = ln(2) + 4 An example for division: e^(x/5) = 2 …Given a logarithmic function with the form f(x) = logb(x + c), graph the translation. Identify the horizontal shift: If c > 0 ,shift the graph of f(x) = logb(x) left c units. If c < 0 ,shift the graph of f(x) = logb(x) right c units. Draw the vertical asymptote x = − c. Identify three key points from the parent function.Oct 10, 2018 · How to graph Natural Logarithmic Functions. We discuss how to graph the parent function natural log (y=lnx) as well as translations of of the basic graph. ... Derivative of Natural log (ln (x)) with Proofs and Graphs. The natural logarithm, also denoted as ln (x), is the logarithm of x to base e (euler’s number). The derivative of the natural logarithm is equal to one over x, 1/x. We can prove this derivative using limits or implicit differentiation. In this article, we will learn how to derive the ...211k 17 135 288. Add a comment. 0. For horizontal asymptotes you have to make x → ∞ and x → − ∞ and f must goes to some constant. lim x → ∞(x − 1)ln(1 − 1 x) = lim x → ∞ln(1 − 1 x) 1 x − 1. By L'Hopital: lim x → ∞ 1 x2 x x − 1 − 1 ( x − 1)2 = lim x → ∞ 1 x ( x − 1) − 1 ( x − 1)2 = lim x → ∞ − ...For problems that add/subtract to/from the x, simply solve for the exponent by using ln. In the example you gave: e^(x-4) = 2 x - 4 = ln(2) x = ln(2) + 4 An example for division: …Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, ...Sure, you have an advanced calculated that can handle complex numbers. While it is usually taught in earlier math courses that the log of a negative number is undefined, that is not true. Here is the actual solution: let k be any number greater than 0. ln (−k) = ln (k) + π𝑖. Thus, ln (−1) = ln (1) + π𝑖. 1 comment. Yes, if we know the function is a general logarithmic function. For example, look at the graph in Try It 11. The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical asymptote. It approaches from the right, so the domain is all points to the right, [latex]\left\{x|x>-3\right\}[/latex].Free online graphing calculator - graph functions, conics, and inequalities interactivelyDownload the the featured file here: https://www.bluepecantraining.com/create-a-logarithmic-graph-in-excel-semi-log-and-log-log/In this video I demonstrate h...Lesson 8: Graphs of logarithmic functions. Graphical relationship between 2ˣ and log₂(x) Graphing logarithmic functions (example 1) ... Even shifting graph by 3 to the left …Double-click on the axis to open the Format Axes dialog. In the Scale section, set the axis to Log10 or Log 2 or Ln (natural logarithm). This graph shows log10 ...May 26, 2020 ... This is a very quick review of how to graph y = ln(x) with the 'e to the x dance in reverse'. For more information, go to ...domain and range ln(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…The derivative of ln(3x) is one over x. The symbol ln is used for a natural log function. The derivative of ln(3x) is expressed as f'(x) equals ln(3x) The expression ln(3x) can be ...I guess we could also skip averaging this value with the difference of ln (x - delta x) and ln (x) (i.e. take upper bound difference directly as the error) since averaging would dis-include the potential of ln (x + delta x) from being a "possible value". Am I wrong or right in my reasoning? $\endgroup$ –The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1 ). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural". Lesson 8: Graphs of logarithmic functions. Graphical relationship between 2ˣ and log₂(x) Graphing logarithmic functions (example 1) ... Even shifting graph by 3 to the left doesn't really make a sense to me, cuz y=2log₂(-(x+3)) should end up in the previous form y=2log₂(-x-3) and then we should have shifted by 3 to the right instead ...where “ln” is the natural logarithm, [A] 0 is the initial concentration of A, and [A] ... This graph shows the plot of the natural logarithm of concentration versus time for a first-order reaction. Example 17.4. The decomposition of a pollutant in water at 15°C occurs with a rate constant of 2.39 y −1, following first-order kinetics. If ...A semi-log graph is a type of graph that uses a linear scale on the x-axis and a logarithmic scale on the y-axis. We often use this type of graph when the values for the y variable have much greater variability compared to the values for the x variable. This type of graph is particularly useful for visualizing percentage change of some variable ...Learn how to graph the functions y=log base 2 of x, y=-log base 2 of x, and y=-log base 2 of (x+2) using the graphical relationship between 2^y and y. See examples, tips, and …We also want to gain an understanding of the graph of a logarithmic function. Consider the graph of \(y=2^x\) from the previous section. Recall that the graph of the inverse of a function is the reflection of the graph of the function about the diagonal line \(y=x\). So in this case we have: The graph can also be obtained using a graphing ... Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step.This function is called the natural logarithm. We derive a number of properties of this new function: Domain = (0; 1) x > 0 if x > 1, ln x = 0 if x = 1, ln x < 0 if x < 1. d(lnx) = 1. dx x. The graph of y = ln x is increasing, continuous and concave down on the interval (0; 1). We de ne a new function. Z x 1 ln x = dt;Send us Feedback. Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step.The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. The formula for natural log is given as, \[\large Product\;Rule: …Graf för ln (x) ln (x) funktionsdiagram. Naturlig logaritmdiagram. y = f ( x) = ln ( x) ln (x) diagramegenskaper. ln (x) definieras för positiva värden på x. ln (x) definieras inte för verkliga icke-positiva värden på x. ln (x) <0 för 0 <x <1; ln (x) = …Review Properties of Logarithmic Functions. We first start with the properties of the graph of the basic logarithmic function of base a, f (x) = log a (x) , a > 0 and a not equal to 1. The domain of function f is the interval (0 , + ∞). The range of f is given by the interval (- ∞ , + ∞). Function f has a vertical asymptote given by the ...Google Spreadsheets is a powerful tool that can help you organize and analyze data effectively. One of its most useful features is the ability to create interactive charts and grap...You can graph now. Note that x cannot be less than -1. graph {ln (x+1) [-5.205, 14.795, -7.04, 2.96]} Answer link. Assigning different values for x and getting y. If your x is zero, your function will be y=ln1 = 0 If your x is 1, your function will be y=ln2 = 0.693 If your x is 2, your function will be y=ln3 = 1.099 etc. You can graph now.Logarithmic Functions. The "basic" logarithmic function is the function, y = log b x, where x, b > 0 and b ≠ 1. The graph of the logarithmic function y = log x is shown. (Remember that when no base is shown, the base is …Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Graf för ln (x) ln (x) funktionsdiagram. Naturlig logaritmdiagram. y = f ( x) = ln ( x) ln (x) diagramegenskaper. ln (x) definieras för positiva värden på x. ln (x) definieras inte för verkliga icke-positiva värden på x. ln (x) <0 för 0 <x <1; ln (x) = …To proceed with drawing the $\ln x$ graph, a few simple steps are required. Read more In regression analysis, the variable that is being predicted is the. In this complete guide, you will learn how to draw the graph of $\ln x$ as well as some interesting facts, definitions, and applications of the given function.A semi-log graph is a type of graph that uses a linear scale on the x-axis and a logarithmic scale on the y-axis. We often use this type of graph when the values for the y variable have much greater variability compared to the values for the x variable. This type of graph is particularly useful for visualizing percentage change of some variable ...The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. The formula for natural log is given as, \[\large Product\;Rule: …Graf ln (x) Funkční graf ln (x). Graf přirozeného logaritmu. y = f ( x) = ln ( x) Vlastnosti grafu ln (x) ln (x) je definován pro kladné hodnoty x. ln (x) není definován pro skutečné ne kladné hodnoty x. ln (x) <0 pro 0 <x <1; ln (x) = 0 pro x = 1; ln (x)/ 0 pro x/ 1; ln (x) pravidlaFor x > 0, y = ln(x) is equivalent to ey = x. We read ln(x) as, “the logarithm with base e of x ” or “the natural logarithm of x. The logarithm y is the exponent to which e must be raised to get x. Since the functions y = ex and y = ln(x) are inverse functions, ln(ex) = x for all x and e =ln ( x) x for x > 0.In this minimal working example, the graph of the natural logarithm function has a blemish between x = 0.5 and x = 0.6, no idea why... Does anyone know how to get rid of that and have a smooth grap...Free online graphing calculator - graph functions, conics, and inequalities interactivelyExplore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. How do you graph #y = ln(x) #? Precalculus Exponential and Logistic Functions Exponential and Logistic Graphs. 1 Answer SCooke Mar 2, 2016 In general, any graph is constructed by plotting the points corresponding to the equation solution on a paper. Use the x-axis for the x value, and the y-axis for the calculated y value.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Dec 21, 2020 · Figure 4.4.4: The graphs of three logarithmic functions with different bases, all greater than 1. Given a logarithmic function with the form f(x) = logb(x), graph the function. Draw and label the vertical asymptote, x = 0. Plot the x- intercept, (1, 0). Oct 10, 2018 · How to graph Natural Logarithmic Functions. We discuss how to graph the parent function natural log (y=lnx) as well as translations of of the basic graph. ... So with that out of the way, x gets as large as 25. So let me graph-- we put those points here. So that is 5, 10, 15, 20, and 25. And then let's plot these. So the first one is in blue. When x is 1/25 and y is negative 2-- When x is 1/25 so 1 is there-- 1/25 is going to be really close to there-- Then y is negative 2. A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way. As opposed to a linear number line in which every unit of distance corresponds to adding by the same amount, on a logarithmic scale, every unit of length corresponds to multiplying the previous value by the same amount.Figure 4.7.4: An exponential function models exponential growth when k > 0 and exponential decay when k < 0. Example 4.7.1: Graphing Exponential Growth. A population of bacteria doubles every hour. If the culture started with 10 bacteria, graph the population as …In math, the term log typically refers to a logarithmic function to the base of 10, while ln is the logarithmic function to the base of the constant e. Log is called a common logar...Nov 3, 2022 · Given a logarithmic function with the form f(x) = logb(x + c), graph the translation. Identify the horizontal shift: If c > 0 ,shift the graph of f(x) = logb(x) left c units. If c < 0 ,shift the graph of f(x) = logb(x) right c units. Draw the vertical asymptote x = − c. Identify three key points from the parent function. The “time” we get back from ln () is actually a combination of rate and time, the “x” from our e x equation. We just assume 100% to make it simple, but we can use other numbers. Suppose we want 30x growth: plug in ln ( 30) and get 3.4. This means: e x = growth. e 3.4 = 30. May 26, 2019 ... A ln(x) graph has a vertical asymptote on the y-axis, it crosses the x-axis at the point (1,0). When the function changes to ln(x+4), all points ...A logarithmic function with both horizontal and vertical shift is of the form (x) = log b (x + h) + k, where k and h are the vertical and horizontal shifts, respectively. Example 6. Graph the logarithmic function y = log 3 (x – 2) + 1 and find the function’s domain and range. Solution. Domain: (2,infinity) Because exponential and logarithmic functions are inverses of one another, if we have the graph of the exponential function, we can find the corresponding log function simply by reflecting the graph over the line y=x, or by flipping the x- and y-values in all coordinate points. Let’s use some graphs from the previous section to illustrate ...Figure 4.7.4: An exponential function models exponential growth when k > 0 and exponential decay when k < 0. Example 4.7.1: Graphing Exponential Growth. A population of bacteria doubles every hour. If the culture started with 10 bacteria, graph the population as …The natural log calculator (or simply ln calculator) determines the logarithm to the base of a famous mathematical constant, e, an irrational number with an approximate value of e = 2.71828.In other words, it calculates the natural logarithm. But, what is the natural logarithm, ln x, of a given number x?This is the power the number e has to be …
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.. Jackfruit taste
Free online graphing calculator - graph functions, conics, and inequalities interactively Natural logarithm function. LN ( x) returns the natural logarithm of the positive number x to base e (e=2.718281828). The argument x must be greater than 0. LN is the inverse function of EXP. ln(ex) = x ln ( e x) = x. The argument x can be a real number, a complex number, or a matrix. When it is a matrix, the function returns a matrix with the ...ln(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…Free online graphing calculator - graph functions, conics, and inequalities interactivelyE′ (x) = ex. In general, d dx(eg ( x)) = eg ( x) g′ (x) Example 1.1.1: Derivative of an Exponential Function. Find the derivative of f(x) = etan ( 2x). Solution: Using the derivative formula and the chain rule, f′ (x) = etan ( 2x) d dx(tan(2x)) = etan ( 2x) sec2(2x) ⋅ 2. Example 1.1.2: Combining Differentiation Rules.3.9: Derivatives of Ln, General Exponential & Log Functions; and Logarithmic Differentiation Expand/collapse global location 3.9: Derivatives of Ln, General Exponential & Log Functions; and Logarithmic Differentiation ... Find the slope of the line tangent to the graph of \(y=log_2(3x+1)\) at \(x=1\). Solution. To find the slope, we must ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step.The higher the base is the more sharply the graph curves. (Note: The actual graphs do not intersect the y-axis. If it looks like they do, it is just because of ...Graph of [latex]y=log{_3}x[/latex]: The graph of the logarithmic function with base [latex]3[/latex] can be generated using the function’s inverse. Its shape is the same as other logarithmic functions, just with a different scale.We use the notation f − 1(x) = logax and say the inverse function of the exponential function is the logarithmic function. Definition 10.4.1: Logarithmic Function. The function f(x) = logax is the logarithmic function with base a, where a > 0, x > 0, and a ≠ 1. y = logax is equivalent to x = ay.Free online graphing calculator - graph functions, conics, and inequalities interactively.The natural log calculator (or simply ln calculator) determines the logarithm to the base of a famous mathematical constant, e, an irrational number with an approximate value of e = 2.71828.In other words, it calculates the natural logarithm. But, what is the natural logarithm, ln x, of a given number x?This is the power the number e has to be …Yes, if we know the function is a general logarithmic function. For example, look at the graph in Try It 11. The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical asymptote. It approaches from the right, so the domain is all points to the right, [latex]\left\{x|x>-3\right\}[/latex].Solution. The logarithmic function is defined only when the input is positive, so this function is defined when 5– 2x > 0 . Solving this inequality, 5 − 2x > 0 The input must be positive − 2x > − 5 Subtract 5 x < 5 2 Divide by -2 and switch the inequality. The domain of f(x) = log(5 − 2x) is (– ∞, 5 2). Exercise 4.4.2.The natural logarithm function of x is generally written as lnx, loge x, or if the base e is implicit, log x. So, Ln (Number) = LOG (Number, e) Where e~= 2.7128. Below is the LN Function Graph. In the LN function graph above, the X-axis indicates the number for which log is to be calculated, and the Y-axis indicates the log values..