# Thread: Logarithm Easy Question Help!

1. ## Logarithm Easy Question Help!

If $\displaystyle lnx^2= 3x$, Find the Value of X.

I am missing a major property. Could someone help me 0ut on this one?!

Thank you

2. Originally Posted by r2d2
If $\displaystyle lnx^2= 3x$, Find the Value of X.

I am missing a major property. Could someone help me 0ut on this one?!

Thank you
Do you mean $\displaystyle ln(x^2)$ or $\displaystyle [ln(x)]^2$

Either way you will need to use an iterative solution

3. I mean $\displaystyle ln(x^2)$

4. Originally Posted by r2d2
I mean $\displaystyle ln(x^2)$
There are actually no real (and possibly no complex) solutions for this equation because the two lines do not meet - see the attached graph

5. well I have the answer is equal to $\displaystyle e^3/2$. Or e^(3/2)

6. Originally Posted by r2d2
well I have the answer is equal to $\displaystyle e^3/2$. Or e^(3/2)
If you sub that back into the original equation you do not get 0

$\displaystyle 2ln(e^{1.5}) \neq 3e^{1.5}$

7. Ok I must have copied the problem wrong.

Here it is: not simplified.

$\displaystyle -x-2x+2xlnx=0$

Solve for x.

8. Originally Posted by r2d2
Ok I must have copied the problem wrong.

Here it is: not simplified.

$\displaystyle -x-2x+2xlnx=0$

Solve for x.

$\displaystyle -x - 2x + 2x\ln{x} = 0$

$\displaystyle -3x + 2x\ln{x} = 0$

$\displaystyle x(-3 + 2\ln{x}) = 0$

$\displaystyle x = 0$ is an invalid solution because of domain reasons.

$\displaystyle \ln{x} = \frac{3}{2}$

$\displaystyle x = e^{\frac{3}{2}}$

9. i also got e^(3/2), you just copied it down wrong the first time,
so ur correct
as;
-x-2x+2xlnx=0
-3x+2xlnx=0
2xlnx=3x
lnx=3x/2x
lnx=3/2
x=e^(3/2)

10. Great! Thank you everybody