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How would I go about getting an exact value for a question like: $\log_8 4$

I know that $8^{2/3} = 4$ but how would I get that from the question?

Alraxite
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user1804933
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1 Answers1

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The logarithm can be rewritten as

$$\log_8(4) = x \iff 8^x = 4$$

Now note that both $8$ and $4$ are powers of $2$ to get

$$(2^3)^x = 2^2$$

or alternatively,

$$2^{3x} = 2^2$$

So $3x = 2$.