Question

usando a definição de logaritmo, calcule : log1/4 16

Answer 1

Pela definição

$\large\fbox{ \ell og_{\alpha}(\beta)=y~\Leftrightarrow~\alpha^y=\beta }~~~~(0\ \textless \ \alpha \neq 1)$

Aplicando a definição

$\large\begin{array}{l}\ell og_{\frac{1}{4}}(16)=y\\\\\\\begin{pmatrix}\dfrac{1}{4}\end{pmatrix}^y=16\\\\\\\begin{pmatrix}4^{-1}\end{pmatrix}^y=4^2\\\\\\4^{-y}=4^2\end{array}$

Lembrando que

$\large\fbox{ a^b=a^c~\Longleftrightarrow~b=c }~~~~(0\ \textless \ a\neq1)$

Portanto

$\large\begin{array}{l}4^{-y}=4^2~\Longleftrightarrow~-y=2\\\\\\\fbox{ y=-2 }\\\\\\\fbox{\fbox{ \ell og_{\frac{1}{4}}(16)=-2 }}\end{array}$