a)
[tex]\bf log_4(x)=3\\\\
-----------------------------\\\\
log_{{ a}}{{ a}}^x\implies x\qquad \qquad
\boxed{{{ a}}^{log_{{ a}}x}=x}\impliedby
\begin{array}{llll}
\textit{we'll use this}\\
\textit{cancellation rule}
\end{array}\\\\
-----------------------------\\\\
4^{\cfrac{}{}log_4(x)}=4^3\implies x=4^3[/tex]
b)
[tex]\bf 3^{2y}=81\qquad
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^{2y}=3^4\impliedby
\begin{array}{llll}
\textit{same base}\\
exponents\\
must\ be\\
the\ same
\end{array}
\\\\\\
2y=4\implies y=\cfrac{4}{2}\implies y=2[/tex]
