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Graphing Logarithmic Functions
Let us study the graph of y = lnx. Here are a few values of y and dy/dx.
The limits as x → 0+ and x → ∞ (see Example 4, Section 8.2) are: From the sign of dy/dx and d2y/dx2 we get the following information.
We use this information to draw the curve in Figure 8.5.2. Figure 8.5.2 There are two bases for logarithms which are especially useful for different purposes, base 10 and base e. The student should be careful not to confuse the two.
To pass back and forth between common and natural logarithm we need the constants log10 e ~ 0.4343, In 10 ~ 2.3026. Then and
Warning: Do not make the mistake of using common logarithms instead of natural logarithms in differentiating and integrating.
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Home Exponential and Logartihmic Functions Natural Logarithms Graphing Logarithmic Functions |