# Math Help - HELP W/ Natural Log

1. ## HELP W/ Natural Log

ln(5x-2) = ln6 - ln(x-3)

Thanks!

2. Originally Posted by felixthecat12b
ln(5x-2) = ln6 - ln(x-3)

Thanks!
Rewrite with you log rules to get

$\ln(5x-2)=\ln\left( \frac{6}{x-3}\right)$

Since both sides are the same natural log the arguments must be equal

$5x-2=\frac{6}{x-3}$ Clearing the fraction we get

$(x-3)(5x-2)=6 \iff 5x^2-17x+6=6 \iff 5x^2-17x=0$

$x(5x-17)=0$ so we get the two solutions $x=0 \\\ x=\frac{17}{5}$

x cannot be zero why? hmmm but the other will work.

I hope this helps.

Good luck.