Question

log p = 1/2(log x - 3 log y)

Answer 1

Lembrando da definição de logaritmo onde:  

$\large\fbox{ \mathsf{y=\ell og_ab~\Leftrightarrow~a^y=b} }$

E considerando p, x e y maiores que zero, teremos o seguinte:

$\mathsf{\ell og(p)=\frac{1}{2}(\ell og(x)-3\ell og(y))}\\\\\\\mathsf{\ell og(p)= \frac{1}{2}(\ell og(x)-\ell og(y)^3)}\\\\\\\mathsf{\ell og(p)=\frac{1}{2}\ell og\begin{pmatrix}\mathsf{\dfrac{x}{y^3}}\end{pmatrix}}\\\\\\\mathsf{\ell og(p)=\ell og\begin{pmatrix}\mathsf{\dfrac{x}{y^3}}\end{pmatrix}}^{\frac{1}{2}}}\\\\\\\fbox{ \mathsf{p=\begin{pmatrix}\mathsf{\dfrac{x}{y^3}}\end{pmatrix}}^{ \frac{1}{2}}~\Leftrightarrow~~\mathsf{p=\sqrt{\dfrac{x}{y^3}}} }}$