SOLUTION: (logx/log2x)=(log4x/log8x) solve for x

Question 280812: (logx/log2x)=(log4x/log8x) solve for x
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(logx/log2x)=(log4x/log8x) solve for x
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(log(x))/[log(2) + log(x)] = [log(4)+log(x)]/[log(8)+log(x)]
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Cross-multiply:
log(x)*log(8) + log(x)^2 = log(2)*log(4) + log(2)*log(x) + log(x)*log(4)
+(log(x))^2
---------------------
Simplify:
Remove log(x)^2
---
log(x)*log(8) = log(2)*log(4) + log(2)*log(x) + log(x)*log(4)
----
log(x)[log(8)-log(2)-log(4)] = log(2)*log(4)
----
log(x) = [log(2)*log(4)]/[log(8)-log(2)-log(4)]
---
log(x) = [log(2)*log(4)]/[log[8/(2*4)]
log(x) = [log(2)*log(4)]/log(1)
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If the arithmetic is correct there is no solution since log(1) = 0
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Cheers,
Stan H.

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