How do you solve $8^x=4$ ?

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Answer 1 · 2017-01-17T00:58:49

$8^x=4 <=> x=2/3$

$8^x=4$

Since $4=(2)(2)=2^2$

we can say that

$8=4(2)=(2)(2)(2)=2(2^2)=2^(2+1)=2^3$

So by changing notation we get

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

and since $(x^a)^b=x^(ab)$ , we can say

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

Then we take the $ln_2(x)$ of both sides

$<=> ln_2(2^(3x))=ln_2(2^2)$

This gives us

$<=> 3x=2$

Then we divide both sides by 3 to isolate x

$<=>x=2/3$

and we have our answer

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