Question
Evaluate $:\log_2 ( 1\div 8 )$
✓
Answer
Let $\log _2 \frac{1}{8}=x$
$\Rightarrow 2^x=\frac{1}{8}$
$ \Rightarrow 2^x=\frac{1}{2 \times 2 \times 2}$
$ \Rightarrow 2^x=\frac{1}{2^3}$
$ \Rightarrow 2^x=2^{-3}$
$ \Rightarrow x=-3$
Thus, $\log _2 \frac{1}{8}=-3$
$\Rightarrow 2^x=\frac{1}{8}$
$ \Rightarrow 2^x=\frac{1}{2 \times 2 \times 2}$
$ \Rightarrow 2^x=\frac{1}{2^3}$
$ \Rightarrow 2^x=2^{-3}$
$ \Rightarrow x=-3$
Thus, $\log _2 \frac{1}{8}=-3$
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