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

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).
RELATED QUESTIONS
lnx - ln(x + 2) = 3 This is what I tried: lnx - ln(x+2) = 3 distributed lnx -... (answered by nerdybill)

Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single... (answered by stanbon,josmiceli)

How can I solve this problem algebraically ln(x + 3) � ln(x � 4) =... (answered by jim_thompson5910,rothauserc)

Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)

"Rewrite the expression 3 ln(4) - 2 ( ln(10) - ln(2) ) in the form ln(x), a single... (answered by jim_thompson5910)

lnx+ln(x+8)=4 i need help on how to solve this step by... (answered by KMST)

Two ln problems I need help with. ln 3 - (ln x + ln 6) = ln x - ln 8 ln 3 + ln 2x = (answered by stanbon)

Simplify logarithms to rewrite the following expressions in terms of u and t. Let ln x=t... (answered by Tatiana_Stebko)

ln5-lnx=3 I tried:... (answered by josmiceli,stanbon,richard1234)