Logarithmic Equation with x on both sides

[Negima]

Exponential Equation with x on both sides

Homework Statement

18x^2=6e^(2x)

Homework Equations

I don't know any for the step I got stuck on.

The Attempt at a Solution

3x^2=e^2x
ln3x^2=lne^2x
2ln3x=2x
ln3x=x

 

[Dick]

Please start using more parentheses, ok? If you mean 3*x^2=e^(2x), then taking logs gives you log(3)+2*log(x)=2*x. The left side is not 2ln3x, whatever that means. You can't solve that using elementary functions. You can prove a solution exists, and you can solve it numerically, but that's about it.

 

[Negima]

Thank you for your reply! And sorry about the lack of parenthesis.

By solving it numerically, do you mean guess and checking values for x? Or actually solving for x?

 

[rock.freak667]

Thank you for your reply! And sorry about the lack of parenthesis.

By solving it numerically, do you mean guess and checking values for x? Or actually solving for x?

Well yes you can guess values using the intermediate value theorem and show that a solution exists.