# How do you solve # log x = x^2 - 2#?

##### 1 Answer

#### Explanation:

This is where it gets messy

There is not elementary way to solve this problem

Probably your best shot at solving this problem is graphing it.And says a a lot about this problem

Fortunately I do have a solution

But first lets see why there is no scope to solve this using logarithmic properties

I am going to raise 10 to the power of each side

Now if you want to try solving this you would probably end up going in cirles

# So here is where the real solution start

Have you heard about the **Lambert W function or product log**

Here is a brief explanation

You can read more about this

HERE

So lets Begin

log

Another thing In your case I am assuming logarithm to be Natural logarithm

Now apply the the Lambert W function on both the sides

Since this is very big calculation I used wolfram alpha

So the 2 roots are