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Chapter 5: Q 76. (page 309)

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places.
$\log_{\sqrt{5}} 8$

Short Answer

Expert verified

$2.584$

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{\sqrt{5}} 8$

02

Step 2. Calculation.

Apply the base change formula and simplify.

$\begin{array}{l} \log_{\sqrt{5}} 8 = \frac{\log 8}{\log \sqrt{5}} \\ = \frac{\log 8}{\frac{1}{2} \log 5} \\ = 2 (\frac{\log 8}{\log 5}) \\ = 2 (1.292) \\ \approx 2.584 \end{array}$

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