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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 28. (page 308)

Use properties of logarithms to find the exact value of each expression. Do not use a calculator.
$e^{\log_{e^{2}} 9}$

Short Answer

Expert verified

The value is 3.

Step by step solution

01

Step 1. Given information.

Consider the given information.

$e^{\log_{e^{2}} 9}$

02

Step 2. Logarithm properties.

The properties are defined as,

$\begin{array}{l} \log_{a} b = \frac{\log b}{\log a} \\ \log_{a} M^{r} = r \log_{a} M \\ a^{\log_{a} (b)} = b \end{array}$

03

Step 3. Calculation.

Apply the properties.

$\begin{array}{l} e^{\log_{e^{2}} 9} = e^{\frac{\log 9}{\log e^{2}}} \\ = e^{\frac{\log 9}{2 \log e}} \\ = e^{\frac{\log_{e} 9}{2}} \\ = e^{\log_{e} \sqrt{9}} \\ = \sqrt{9} \\ = 3 \end{array}$

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Most popular questions from this chapter

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

$f (x) = \frac{2}{3 + x}$

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