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

Thanks!

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- Jun 9th 2008, 10:17 PMfelixthecat12bHELP W/ Natural Log
ln(5x-2) = ln6 - ln(x-3)

Thanks! - Jun 9th 2008, 10:22 PMTheEmptySet
Rewrite with you log rules to get

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

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

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

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

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

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

I hope this helps.

Good luck.