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

Given expression

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

Concept used

By property of logarithmic function,

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

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

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

Conclusion

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

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

Short Answer

Step by step solution

Given expression

Concept used

Evaluate

Conclusion

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Evaluate each expression. Do not use a calculator.log218

Short Answer

Step by step solution

Given expression

Concept used

Evaluate

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

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Study anywhere. Anytime. Across all devices.

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