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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.19 (page 349)

Evaluate each expression. Do not use a calculator.
$\log_{2} (\frac{1}{8})$

Short Answer

Expert verified

$\log_{2} (\frac{1}{8}) = - 3$

Step by step solution

01

Given expression

The expression is: $\log_{2} (\frac{1}{8})$

02

Concept used

By property of logarithmic function,

$\log_{a} x^{n} = n \log_{a} x$
$\log_{a} a = 1$

03

Evaluate

$\log_{2} (\frac{1}{8}) = \log_{2} (\frac{1}{2^{3}})$

$\log_{2} (\frac{1}{8}) = \log_{2} {(2^{3})}^{- 1}$

$\log_{2} (\frac{1}{8}) = \log_{2} 2^{(- 3)}$ ; Applying property of radicals

$\log_{2} (\frac{1}{8}) = - 3 \log_{2} 2$ ; Applying property of logarithmic function

role="math" localid="1646475559678" $\log_{2} (\frac{1}{8}) = - 3 路 1$ ; Applying property of logarithmic function

$\log_{2} (\frac{1}{8}) = - 3$

04

Conclusion

Thus, $\log_{2} (\frac{1}{8}) = - 3$

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