Chapter 11.4, Problem 35E

To determine

The solution of the expression.

Answer to Problem 35E

  $x=\frac{7}{2}$ .

Explanation of Solution

Given information:

Evaluate the expression:

  ${\log }_{4}128$

Calculation:

The given expression is ${\log }_{4}128$ .

Let $x={\log }_{4}128$

By the defination of the logarithm

  $4^x=128$

Write $4$ as a $2^2$ and $128$ as $2^7$ :

  ${(2^2)}^x=2^7$

By power of power rule:

  $2^{2x}=2^7$

If $a^u=a^v$ then $u=v$ ,

  $2x=7$

Divide both side by $2$ :

  $x=\frac{7}{2}$

Thus, the solution is $x=\frac{7}{2}$ .