SOLUTION: solve exactly (lnx)^3= lnx^9

Question 110930: solve exactly
(lnx)^3= lnx^9
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let

So we get

Rewrite the logarithm using the identity

Replace with w

Subtract 9w from both sides

Factor out a w

Factor using the difference of squares

So our solutions are (in terms of w)

, , or

So this means , , or

Now raise all sides as an exponent with base e

, , or

Simplify

, , or
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