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Chapter 5: Q 34. (page 298)

Find the exact value of the logarithm without using a calculator.

log39

Short Answer

Expert verified

The exact value of the logarithm is 4.

Step by step solution

01

Step 1. Given information

A logarithmic function is given aslog39.

02

Step 2. Formula Used

The logarithmic function y=logax can be changed into an exponential statement as x=ay.

03

Step 3. Finding Value of the logarithm

Considerlog39=x

By changing rule of logarithm to exponential function,

3x=93x=34x=4log39=4

The required value is,

log39=4

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Most popular questions from this chapter

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

y=2x+1

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=2x+3x+2

Begin with the graph of y=ex and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=-ex

solve each equation. Verify your results using a graphing utility.

ex=e3x+8

Do you think that there is a power function that increases

more rapidly than an exponential function whose base is greater than 1 ? Explain.
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