Question

log $\sqrt{8}$ 4

Answer 1

$log_{n}(n)=1\\\\log_{(b^{n})}a=\frac{1}{n}*log_{b}(a)\\\\log_{b}(a^{n})=n*log_{b}(a)$
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$log_{4}(\sqrt{8})=log_{(2^{2})}(\sqrt[2]{2^{3}})\\\\log_{4}(\sqrt{8})=\frac{1}{2}*log_{2}(\sqrt[2]{2^{3}})\\\\log_{4}(\sqrt{8})=\frac{1}{2}*log_{2}(2^{\frac{3}{2}})\\\\log_{4}(\sqrt{8})=\frac{1}{2}*\frac{3}{2}*log_{2}(2)\\\\log_{4}(\sqrt{8})=\frac{3}{4}*1\\\\\boxed{\boxed{log_{4}(\sqrt{8})=\frac{3}{4}}}$