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## Homework Statement

3x^[tex]^{2}[/tex] = e^[tex]^{2x}[/tex] --- solve for x.

## Homework Equations

I burned it down to ln3 + 2lnx = 2x

EDIT - you can also square root each side and get it down to x = ln([tex]\sqrt{3}[/tex]x)

## The Attempt at a Solution

ln(3x^2) = 2x

ln3 + 2lnx = 2x

(ln3)/2 = x - lnx

I vaguely remember this problem earlier in the year. Yes, it can/should be done without a calculator, although I'm stuck at what I posted. There may be a special "trick" at the beginning that doesn't actually require this type of algebra. Alas, I cannot figure it out!

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