# SOLUTION: I need helping solving this for x: (ln x)^3=ln x^4 Can I rewrite it as (ln x)^3=4lnx ? Then can I divide both sides by lnx leaving (ln x)^2=4 ? Can I now square both sides leav

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need helping solving this for x: (ln x)^3=ln x^4 Can I rewrite it as (ln x)^3=4lnx ? Then can I divide both sides by lnx leaving (ln x)^2=4 ? Can I now square both sides leav      Log On

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 Question 61154: I need helping solving this for x: (ln x)^3=ln x^4 Can I rewrite it as (ln x)^3=4lnx ? Then can I divide both sides by lnx leaving (ln x)^2=4 ? Can I now square both sides leaving me with ln x=2 ? Now I'm not sure what to do next.Answer by mathick(4)   (Show Source): You can put this solution on YOUR website!I need helping solving this for x: (ln x)^3=ln x^4 Can I rewrite it as (ln x)^3=4lnx ? Yes. Then can I divide both sides by lnx leaving (ln x)^2=4 ? Yes, but this assumes that you're not dividing both sides by 0, i.e. that ln(x) is not 0. This step wouldn't be valid in the case that ln(x) = 0, so this case (ln(x) = 0) needs to be treated separately. Can I now square (root) both sides leaving me with ln x=2 ? Right, ln (x) = 2, and also ln(x) = -2. (Taking the square root of both sides gives ln x = +2 and ln x = -2.) Now I'm not sure what to do next To solve ln(x) = 2 for x, exponentiate both sides: . The left side simplifies, giving one of the final answers: . The equation ln (x) = -2 can be solved similarly. Finally, there is the case when ln(x) = 0. This happens when x = 1. To verify that this is a solution, you can plug it into the original equation and see if it checks out (gives a true equation).