Chapter 8.4, Problem 49STP

To determine

The solution of the expression.

Answer to Problem 49STP

  ${\log }_{4}256=4$ .

Explanation of Solution

Given information:

Solve:

  ${\log }_{4}256$

Calculation:

The given expression is ${\log }_{4}256$ .

To solve the logarithmic equation by using the defination of a logarithm are as shown below:

  $\begin{array}{l}{\log }_{4}256\text{ {The original equation}}\\ 256=4^y\text{ {Defination of logarithm} }\\ 4^4=4^y{\text{ {256=4}}^4\text{}}\\ y=4\end{array}$

Thus, ${\log }_{4}256=4$ .