how do you solve 8^ log base 2 of 5

$$8^{log_2 5}\\\\
=(2^3)^{log_2 5}\\\\
=2^{3log_2 5}\\\\
=2^{log_2 5^3}\\\\
=2^{log_2 125}\\\\
=125\\\\$$

 And that is exact. 

how do you solve 8^ log base 2 of 5

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So, I'm assuming you have this:

8^(log₂(5))

By something called the "change of base" rule, we can write:

log₂(5)   =    [ log(5) / log (2) ]

And evaluating this gives us......2.3219280948873626

So we have

8^{2.3219280948873626} ≈ 125

And that's it.....