Chapter 8.2, Problem 1ACYP

To determine

To calculate: The value of n in the equation $4^{2n-1}=64$ .

Answer to Problem 1ACYP

The value of n in the equation $4^{2n-1}=64$ is 2.

Explanation of Solution

Given information:

The given equation is $4^{2n-1}=64$ .

Formula used:

Property of equality of exponential functions:

If $b^x=b^y$ then $x=y$for all $b>0$ and $b\ne 1$ .

Calculation:

Consider the given equation,

  $4^{2n-1}=64$

Rewrite the above equation as like this,

  $4^{2n-1}=4^3$

Now, apply the property of equality of exponential functions:

  $\begin{array}{c}{4}^{2n-1}=4^3\\ 2n-1=3\\ n=\frac{3+1}{2}\\ n=2\end{array}$

Therefore, the value of n in the equation $4^{2n-1}=64$ is 2.