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

A. 1/2X

B. X-1/4

C. X-1/3

D. X-1/2

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This answer was edited.Correct Answer: Option C

Log 5 base 8 log 2 base 8 = X. Are u with me? we must be careful here. Can you still remember the rule that says loga^2 base a^3 gives 2/3 log a base a which is eaqual to 2/3 X 1 = 2/3.

so let’s apply d same thing here, log 2 ^1 base 8. Do not forget that 8 can also be written as 2^3.

You got it? If u are with me, am sure you’re understanding a little bit.

So we have log 2^1 base 2 ^3 to be 1/3 log 2 base 2 which will now give us 1/ 3 X 1 = 1/3.

Recall that we say log5 base 8 X log 2 base 8 = X.

Now that we know our log 2 base 8 = 1/3, so we put into d equation to have..

Log 5 base 8 1/ 3 = X.

Therefore, log 5 base 8 = X – 1/3.