# Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises: 34

(a) The natural logarithm is the logarithm with the base equal to Euler's number $e$: (b) The common logarithm is the logarithm with the base equal to $10$. (c) The graphs are shown on the figure below (exponential is blue and the logarithm is red). The line $y=x$ is dashed.

#### Work Step by Step

(a) The natural logarithm is the logarithm with the base equal to Euler's number $e$: $$\ln x =\log_{e}x.$$ (b) The common logarithm is the logarithm with the base equal to $10$: $$\log x= \log_{10}x$$ (c) The graph of the natural logarithm is obtained by reflecting the natural exponential function abour $y=x$ line and they are shown on the figure below (exponential is blue and the logarithm is red). The line $y=x$ is dashed.

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