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Chapter 5: Q 105. (page 309)

If $f (x) = \log_{a}$ , show that $- f (x) = \log_{1 / a} x$

Short Answer

Expert verified

The result is shown in the explanation.

Step by step solution

01

Step 1. Given information.

Consider the given function.

$f (x) = \log_{a} x$

02

Step 2. Calculation.

Simplify the function to obtain the result.

$\begin{array}{l} - f (x) = - \log_{a} x \\ = \frac{\log x}{- \log a} \\ = \frac{\log x}{\log a^{- 1}} \\ = \frac{\log x}{\log \frac{1}{a}} \\ = \log_{1 / a} x \end{array}$

Since the left side is equal to the right side.
The given equation has been proved.

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Most popular questions from this chapter

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False

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and verify your results using a graphing utility.

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