# Thread: ln and e

1. ## ln and e

The question is:

Given that $\displaystyle \ln(2x^2+9x-5)=1+\ln(x^2+2x-15)$, find $\displaystyle x$ in terms of $\displaystyle e$

I got as far as:

$\displaystyle e = \dfrac{2x-1}{x-3}$

The next step is

$\displaystyle e = \dfrac{2x-1}{x-3} \Rightarrow 3e - 1 = x(e - 2)$

I'm probably just being dense, but I don't know how to do that step. Could somebody please help me.

Thank you

2. ## Re: ln and e

$\displaystyle x = \frac{3e - 1}{e - 2}$

and your work is correct.

3. ## Re: ln and e

Originally Posted by icemanfan
$\displaystyle x = \frac{3e - 1}{e - 2}$

and your work is correct.
Thanks for your reply. I see the last step, but I don't know how to do the step I've shown in original post.

4. ## Re: ln and e

Originally Posted by Furyan
The question is:

Given that $\displaystyle \ln(2x^2+9x-5)=1+\ln(x^2+2x-15)$, find $\displaystyle x$ in terms of $\displaystyle e$

I got as far as:

$\displaystyle e = \dfrac{2x-1}{x-3}$

The next step is

$\displaystyle e = \dfrac{2x-1}{x-3} \Rightarrow 3e - 1 = x(e - 2)$

I'm probably just being dense, but I don't know how to do that step. Could somebody please help me.

Thank you
$\displaystyle e = \dfrac{2x-1}{x-3}$

Multiply through by $\displaystyle (x-3)$:

$\displaystyle e(x-3)=2x-1$

Expand:

$\displaystyle ex-3e=2x-1$

Rearrange, so that terms involving an "$\displaystyle x$" are isolated on one side of the equation:

$\displaystyle ex-2x=3e-1$

Factor:

$\displaystyle x(e-2)=3e-1$

5. ## Re: ln and e

Originally Posted by Quacky
$\displaystyle e = \dfrac{2x-1}{x-3}$

Multiply through by $\displaystyle (x-3)$:

$\displaystyle e(x-3)=2x-1$

$\displaystyle ex-3e=2x-1$

Rearrange, so that terms involving an "$\displaystyle x$" are isolated on one side of the equation:

$\displaystyle ex-2x=3e-1$

Factor:

$\displaystyle x(e-2)=3e-1$
Thanks Quacky for taking the time to reply, that was what I was asking. Normally I'd see that, I assumed the rearrangment was some mysterious property of $\displaystyle e$. All these new numbers are scaring the sense out of me , although it was very late, I have so got to get a grip.

Thanks again