QuestionSimplify the expression without using a calculator. $$\log _{\frac{1}{2}}\left(\frac{1}{128}\right)=$$ $\square$ $\square \log _{\square} \square$

Studdy Solution
Use the property of logarithms $\log_b(b^x) = x$ to simplify:
$\log_{\frac{1}{2}}\left(\frac{1}{128}\right) = \log_{\frac{1}{2}}\left(\left(\frac{1}{2}\right)^7\right)$
According to the property, this simplifies to:
$7$
The simplified expression is:
$\boxed{7}$