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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
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ANSWER

[tex]x = 248[/tex]

EXPLANATION

The given logarithmic equation is,

[tex]4 log_{4}(x + 8) = {4}^{2} [/tex]


We divide through by 4 to get,


[tex]log_{4}(x + 8) = 4[/tex]

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

[tex]x + 8 = {4}^{4} [/tex]

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

[tex]x + 8 = 256[/tex]

We group like terms to obtain,

[tex]x = 256 - 8[/tex]

This simplifies to,

[tex]x = 248[/tex]
The value of x is 248.