Question

1- Calcule: a) log: 16 b) log2 128 c) log 0,1 d) Slog: 20 e) log, z 2​

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Answer 1

$\large\boxed{\begin{array}{l}\sf a)~\ell og_{\frac{1}{4}}16=\ell og_{2^{-2}}2^{4}=\dfrac{4}{-2}=-2\\\\\sf b)~\rm \ell og_2\sqrt{128}=\ell og_{2^1}2^{\frac{7}{2}}=\dfrac{\frac{7}{2}}{1}=\dfrac{7}{2}\\\\\sf c)~\rm \ell og0,1=\ell og10^{-1}=-1\ell og10=-1\\\\\sf d)~\rm 5^{\ell og_520}=20\\\\\sf e)~\rm \ell og_{\sqrt{2}}2=\ell og_{2^{\frac{1}{2}}}2^1=\dfrac{1}{\frac{1}{2}}=1\cdot2=2\end{array}}$