Question

What is the solution to 4log4(x+8)=4^2

Answer 1

ANSWER

$x = 248$

EXPLANATION

The given logarithmic equation is,

$4 log_{4}(x + 8) = {4}^{2}$


We divide through by 4 to get,


$log_{4}(x + 8) = 4$

Let us take the antilogarithm of both sides to base 4 to obtain,

$x + 8 = {4}^{4}$

We evaluate the expression on the right hand side to obtain,

$x + 8 = 256$

We group like terms to obtain,

$x = 256 - 8$

This simplifies to,

$x = 248$
The value of x is 248.

Answer 2

Assuming that's log base 4

4log4(x+8) = 4^2
log4(x+8) = 4^2/4
log4(x+8) = 4
x+8 = 4^4
x+8 = 256
x = 256 - 8
x = 248