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)

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

6 0

4 years ago

(8x10^-3)+(2 x 10^-4)​

(8x10^-3)+(2 x 10^-4)