If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.

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Explanation

log810 = X = log82x5

log82 + log85 = X

Base 8 can be written as 23

log82=y

therefore 2=8y

y=13

13=log82

taking 13 to the other side of the original equation

log85=X−13