Rewrite each equation as requested. (a) Rewrite as an exponential equation. log_(3)(1)/(81)=-4 (b) Rewrite as a logarithmic equation. 8^1=8 (a) square ^square =square (b) log_(square )square =square

(a) Rewrite.<br />$log_{3}\frac {1}{81}=-4$<br /><br />To rewrite the given logarithmic equation as an exponential equation, we can use the formula:<br /><br />$log_{b}x=y$ is equivalent to $b^y=x$<br /><br />In this case, we have:<br />- Base (b) = 3<br />- Exponent (y) = -4<br />- Argument (x) = $\frac{1}{81}$<br /><br />Using the formula, we can rewrite the equation as:<br /><br />$3^{-4}=\frac{1}{81}$<br /><br />Therefore, the exponential equation is:<br /><br />$3^{-4}=\frac{1}{81}$<br /><br />(b) Rewrite as a logarithmic equation.<br />$8^{1}=8$<br /><br />To rewrite the given exponential equation as a logarithmic equation, we can use the formula:<br /><br />$b^y=x$ is equivalent to $log_{b}x=y$<br /><br />In this case, we have:<br />- Base (b) = 8<br />- Exponent (y) = 1<br />- Argument (x) = 8<br /><br />Using the formula, we can rewrite the equation as:<br /><br />$log_{8}8=1$<br /><br />Therefore, the logarithmic equation is:<br /><br />$log_{8}8=1$