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zysi [14]
3 years ago
6

How do you solve these problems?

Mathematics
1 answer:
Rzqust [24]3 years ago
6 0
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
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