Question

How do you solve these problems?

Answer 1

A)

$\bf log_4(x)=3\\\\ -----------------------------\\\\ log_{{ a}}{{ a}}^x\implies x\qquad \qquad \boxed{{{ a}}^{log_{{ a}}x}=x}\impliedby \begin{array}{llll} \textit{we'll use this}\\ \textit{cancellation rule} \end{array}\\\\ -----------------------------\\\\ 4^{\cfrac{}{}log_4(x)}=4^3\implies x=4^3$

b)

$\bf 3^{2y}=81\qquad \begin{cases} 81=3\cdot 3\cdot 3\cdot 3\\ \qquad 3^4 \end{cases}\implies 3^{2y}=3^4\impliedby \begin{array}{llll} \textit{same base}\\ exponents\\ must\ be\\ the\ same \end{array} \\\\\\ 2y=4\implies y=\cfrac{4}{2}\implies y=2$