Question

7. Evaluate \ \frac{1}{8} " alt=" log_2 \ \frac{1}{8} " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

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

Step-by-step explanation:

Think of Log as a complimentary operation to powers.

$log_{2}( \frac{1}{8} )$

means you need to find the exponent of 2 that yields 1/8.

As this number is putting the base on the denominator, we know for a fact it must be some negative number, or

${2}^{ - x} = \frac{1}{ {2}^{x} }$

Then, by trial and error works just fine, going through the powers of 2.

${2}^{-2} = \frac{1}{ {2}^{2} } = \frac{1}{4} \\ {2}^{-3} = \frac{1}{{2}^{3} } = \frac{1}{8}$

And that is it.