logarithmic equation, different bases and fractional co-eff

[jandrisle]

I am having the hardest time solving this equation and it is really holding me back from understanding the rest of the material pertaining to logarithms. Thanks!

. . .(1/3) log₂(x²) = log₈(2x)

When I try to complete the equations by distributing by power rule, I either get a third degree polynomial or a unsolvable quadratic equation. I know from my text what the answer is, but can't figure out the right sequence of steps.
(Sorry I couldn't do sub and super-script for the format)
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Edited by stapel -- Reason for edit: inserting formatting

 

[stapel]

Since 8 is a power of 2, you could try converting to that:

. . . . .log₈(2x) = [log₂(2x)] / [log₂(8)] = [log₂(2x)] / 3

...by the change-of-base formula. Then you have:

. . . . .(1/3) log₂(x²) = (1/3) log₂(2x)

Multiply through by 3, and then equate the arguments, and that should do the trick.

Eliz.