Question
Evaluate $:\log_{0.5}16$
✓
Answer
Let $\log _{0.5} 16=x$
$\Rightarrow 0.5^x=16$
$ \Rightarrow\left(\frac{5}{10}\right)^x=2 \times 2 \times 2 \times 2$
$\Rightarrow\left(\frac{1}{2}\right)^x=2^4$
$\Rightarrow \frac{1}{2^x}=2^4$
$\Rightarrow 2^{-x}=2^4$
$ \Rightarrow-x=4$
$ \Rightarrow \mathrm{x}=-4$
Thus, $\log _{0.5} 16=-4$
$\Rightarrow 0.5^x=16$
$ \Rightarrow\left(\frac{5}{10}\right)^x=2 \times 2 \times 2 \times 2$
$\Rightarrow\left(\frac{1}{2}\right)^x=2^4$
$\Rightarrow \frac{1}{2^x}=2^4$
$\Rightarrow 2^{-x}=2^4$
$ \Rightarrow-x=4$
$ \Rightarrow \mathrm{x}=-4$
Thus, $\log _{0.5} 16=-4$
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