Question

solve each of the following equations

Answer 1

In the question, we are asked to solve the indicial equation below;

$(\frac{1}{16})^{3x-1}=32$

Explanation

We will simplify the given equation into similar exponentials.

$(\frac{1}{2^4})^{3x-1}=2^5$

Next we have;

$\begin{gathered} (2^{-4})^{3x-1}=2^5 \\ ^{}\text{ Using the laws of indices (a}^m)^n=a^{mn} \\ 2^{-4(3x-1)}=2^5 \\ 2^{-12x+4}=2^5 \\ \therefore-12x+4=5 \\ -12x=1 \\ x=-\frac{1}{12} \end{gathered}$

Answer:

$x=\frac{-1}{12}$