Hi, I'm having some issues with this problem:

$\displaystyle f(x) = -2e^{5x}+6$

I need to solve for the x intercept of the graph of f.

I tried to do it like so:

$\displaystyle 0 = -2e^{5x}+6$

$\displaystyle 2e^{5x} = 6$

$\displaystyle \log(2e^{5x}) = \log(6)$

$\displaystyle 5x\log(2e) = \log(6)$

$\displaystyle 5x = \frac{\log(6)}{\log(2e)}$

$\displaystyle x = \frac{\frac{\log(6)}{\log(2e)}}{5}$

That gives me: .2116484012

Using my graphing calculator to get the intersection of:

$\displaystyle y1 = -2e^{5x}+6$

$\displaystyle y2 = 0$

Gives an answer of: .21972246

Would someone mind explaining what I've done wrong? Thanks!