Thread: Solving problems with natural logs

1. Solving problems with natural logs

$\ln(x^2)=10$

I know how to solve this by turning it into an exponential form ie.

$e^{10}=x^2$

and solving from there but can you do something like this

$e^{\ln(x^2)}=e^{10}$

$e^{2\ln(x)}=e^{10}$

I don't know what to do from here.

2. Re: Solving problems with natural logs

If $e^{2\ln(x)}=e^{10}$ You can put their indexes equal to each other so $2ln(x)=10$

3. Re: Solving problems with natural logs

Where would I go from there? Does that get me any closer to solving for x? Sorry if I'm missing what you are getting at.

4. Re: Solving problems with natural logs

From $2ln(x)=10$ you can continue
$ln(x)=5$
$x=e^5$

And you get the same answer as your first method

5. Re: Solving problems with natural logs

Ah, I see. Apparently I'm a little rusty at this stuff. Thanks for the help.

6. Re: Solving problems with natural logs

You should brush up on your log properties.

$\log_b{a^n} = n \log_b{a}$ would have saved you time