Question

Log de N na base √2=4

Log de 81 na base a=4

Answer 1

Lembrando da definição de logaritmo, onde:

$\fbox{ a^x=b~\Leftrightarrow~x=\ell og_a~b }~~~a,b\in\mathbb{R},~~0\ \textless \ a \neq 1~~e~~b\ \textgreater \ 0$

Teremos o seguinte:

$\ell og_{\sqrt{2}}(N)=4~\Leftrightarrow~\begin{pmatrix}\sqrt{2}\end{pmatrix}^4=N~\Leftrightarrow~\begin{pmatrix}2^{\frac{1}{2}}\end{pmatrix}^4=N~\Leftrightarrow~2^{\frac{1}{2}\cdot4}=N\\\\2^{\frac{4}{2}}=N~\Leftrightarrow~2^2=N~\Leftrightarrow~\fbox{ N=4 }$


$\ell og_a(81)=4~\Leftrightarrow~a^4=81~\Leftrightarrow~a^4=9^2~\Leftrightarrow~a^4=\begin{pmatrix}3^2\end{pmatrix}^2~\Leftrightarrow~a^4=3^{2\cdot 2}\\\\a^4=3^4~\Leftrightarrow~\fbox{ a=3 }$