Question

Solve each of the following equations

Answer 1

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

`((1)/(16))^(3x-1)=32`

Step-by-step explanation

We will simplify the given equation into similar exponentials.

`((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=-(1)/(12) \end{gathered}`

Answer:

`x=(-1)/(12)`