Question
Evaluate : $\log_{16}8$
✓
Answer
$\text { Let } \log _{16} 8=x$
$ \Rightarrow 16^x=8$
$ \Rightarrow(2 \times 2 \times 2 \times 2)^x=2 \times 2 \times 2$
$ \Rightarrow\left(2^4\right)^x=2^3$
$ \Rightarrow 2^{4 x}=2^3$
$ \Rightarrow 4 x=3$
$ \Rightarrow x=\frac{3}{4}$
Thus, $\log _{16} 8=\frac{3}{4}$
$ \Rightarrow 16^x=8$
$ \Rightarrow(2 \times 2 \times 2 \times 2)^x=2 \times 2 \times 2$
$ \Rightarrow\left(2^4\right)^x=2^3$
$ \Rightarrow 2^{4 x}=2^3$
$ \Rightarrow 4 x=3$
$ \Rightarrow x=\frac{3}{4}$
Thus, $\log _{16} 8=\frac{3}{4}$
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