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Chapter 1: Q38E (page 7)

(a) What is the natural logarithm?

(b) What is the common logarithm?

(c) Sketch the graph of the natural logarithm function and the natural exponential function with a common set of axes.

Short Answer

Expert verified

a) The logarithmic function with base \(e\) is called the natural logarithm and is denoted by \(\ln x\).

b) The logarithmic function with base \(10\) is called the common logarithm and is denoted by \(\log x\).

c) The graph of the natural logarithm function and natural exponential logarithm function is shown below:


Step by step solution

01

Explain the natural logarithm

a)

If the base of thelogarithmic functionis\(e\), then itis known as thenatural logarithmand is represented by \(\ln x\).

02

Explain the common logarithm

b)

If the base of thelogarithmic functionis 10, then it is known as thecommon logarithm and is represented by \(\log x\).

03

Sketch the graph of the natural logarithm and natural exponential function

c)

Sketch the graph of the natural logarithm function and natural exponential function as shown below:

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