Question

Precalculus

Given the exponential equation:,(see image) find a common base and solve for x.

Images of 4 answers and image of the problem are included.

Thanks!!

Answer 1

`\bf 4^(-x)=\sqrt[8]{\cfrac{1}{32}}\qquad \begin{cases} 4=2^2\\ 32=2^5 \end{cases}\implies (2^2)^(-x)=\sqrt[8]{\cfrac{1}{2^5}} \\\\\\ 2^(-2x)=\sqrt[8]{2^(-5)}\implies 2^(-2x)=2^{(-5)/(8)}\impliedby \begin{array}{llll} \textit{same base, thus the}\\ \textit{exponents must the same} \end{array} \\\\\\ -2x=-\cfrac{5}{8}\implies \boxed{x=\cfrac{5}{16}}`