# Thread: help with natural logs and logs based of 10

1. ## help with natural logs and logs based of 10

My teacher told the tutors at my school not to help us on are homework and I don't have enough money to get a tutor
so this is my only hope. I don't how to start on this.

2. ## Re: help with natural logs and logs based of 10

$e^x-6e^{-x}-1=0$

Multiply every term by $e^x$ ...

$e^{2x}-6-e^x=0$

$e^{2x}-e^x-6=0$

let $u=e^x$ and solve the resulting factorable quadratic equation.

Got you started ... finish it.

3. ## Re: help with natural logs and logs based of 10

I think I got it right

4. ## Re: help with natural logs and logs based of 10

Originally Posted by dtdj13
I think I got it right
uh, no ... you didn't.

5. ## Re: help with natural logs and logs based of 10

$\left| \begin{array}{l}e^{2x}-e^x-6=0\\(e^x-3)(e^x+2)=0\\e^x=3~~\&~~e^x=-2\end{array} \right.$

But it is impossible for $e^x$ to be negative, so there is but one answer: $x=\log(3)$.