Solve the exponential equation. 8^3x =32

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Solve the exponential equation. 8^3x =32

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1433325126056:dw|
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here are some hints :) |dw:1433325279296:dw|

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firstly simplify |dw:1433325406385:dw|
512?
3 times 3x does not equal to 512.. 3 * 3x = 3 * 3 * x = ? So what does 3 times 3 equal to?
oh sorry lol.. 9
i put the equation you drew into my calculator and it said 512 haha
yes so 3* 3x = 3* 3 * x = 9*x = 9x. Therefore we know:|dw:1433326014799:dw| Since the base numbers are the SAME (both are base 2) This means the exponents (power) must be EQUAL.... therefore: |dw:1433326054143:dw|
*therefore divide both sides by 9 to find x.
okay so the answer is \[\frac{ 5 }{ 9 }\] !
that's corrreect :)
I know question is already done. But alternatively you can use the "change of base" method So you have 8 ^ 3x = 32 -> Log both sides ln8^3x = ln32 -> Move the log to the other side, by bring the power down 3x = ln(32) / ln(8) -> Divide the RHS by 3 x = [ln(32)/ln(8)] / 3 = 0.5555556 ~ 5/9
haha that's also true :) Nice job!
yeah haha XD No problem, its lovely how Mathematics can be solved with different methods.
thank you both!

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