Question

(a) rewrite as an exponential equation(b) rewrite as a logarithmic equation

Answer 1

Given:

a)

$\log _3\frac{1}{81}=-4$

For logarithmic equation,

$\begin{gathered} \log _b(x)=y \\ \text{The exponential form is } \\ b^y=x \\ \text{Here, b=3,x=}\frac{1}{81}\text{ and y=-4} \\ 3^{-4}=\frac{1}{81}\text{ is the exponential equation for the given logarithmic equation.} \end{gathered}$

b)

$\begin{gathered} 8^1=8 \\ \text{For the equation a}^x=b\text{ is written in the logarithmic equation as,} \\ \log _a(b)=x \\ Here,a=8,b=8,x=1 \\ \log _88=1 \end{gathered}$

Answer:

$\begin{gathered} a)\text{ }3^{-4}=\frac{1}{81}\text{ } \\ b)\text{ }\log _8(8)=1 \end{gathered}$