# Math Help - e and ln Problem

1. ## e and ln Problem

$3e^{3x} = 3x^{2}$

$\dfrac{3e^{3x}}{3} = \dfrac{3x^{2}}{3}$

$e^{3x} = x^{2}$

$\ln(e^{3x}) = \ln(x^{2})$

$3x = \ln(x^{2})$ - What trick could I do here?

2. ## Re: e and ln Problem

remember laws of logarithms
log(a^m) = m log a

3. ## Re: e and ln Problem

Originally Posted by Jason76
$3e^{3x} = 3x^{2}$

$\dfrac{3e^{3x}}{3} = \dfrac{3x^{2}}{3}$

$e^{3x} = x^{2}$
Write that as $f(x)=e^{3x}-x^2$. Look at the graph.

Use a numerical method such as Newton's approximation to find the root.