Solve for x in: e^(2 ln(x)- ln(x^2+x-3)) = 1 I took the natural log of both sides, and simplified. Here is what I've gotten it down to: 2ln(x)=ln(x^2+x−3) And I'm not sure if you can raise e to the power of each side with that 2 there. Thanks in advance.

Rihanna Bentley

Rihanna Bentley

Answered question

2022-11-09

Solve for x in: e 2 ln ( x ) ln ( x 2 + x 3 ) = 1
I took the natural log of both sides, and simplified. Here is what I've gotten it down to:
2 ln ( x ) = ln ( x 2 + x 3 )
And I'm not sure if you can raise e to the power of each side with that 2 there. Thanks in advance.

Answer & Explanation

Raven Hawkins

Raven Hawkins

Beginner2022-11-10Added 19 answers

You can't exponentiate both sides just yet (well, you can, but I'd rather not), let's see what you can do instead using 2 ln x = ln x 2 giving us
ln x 2 = ln ( x 2 + x 3 ) .
Now you can raise e to the power of each side (exponentiate each side) and get x 2 = x 2 + x 3 which is solvable and gives x = 3. Let's see if this works:
e 2 ln 3 ln 9 = e 0 = 1.
So that definitely works!
gfresh86iop

gfresh86iop

Beginner2022-11-11Added 3 answers

2 ln ( x ) = ln ( x 2 + x 3 ) so ln ( x 2 ) = ln ( x 2 + x 3 ) so x 2 = x 2 + x 3. Added later : Notice that we must have x > 0 and x 2 + x 3 > 0, so 3 is an acceptable value!.

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