logritmic equations

log(3x-9)=log(2x+6)

\(\begin{array}{|rcll|} \hline \log(3x-9)&=& \log(2x+6) \\ 3x-9 &=& 2x+6 \quad &| \quad -2x \\ x -9 &=& 6 \quad &| \quad +9 \\ x &=& 15 \\ \hline \end{array}\)

Solve for x:
log(3 x - 9) = log(2 x + 6)

Subtract log(2 x + 6) from both sides:
log(3 x - 9) - log(2 x + 6) = 0

log(3 x - 9) - log(2 x + 6) = log(1/(2 x + 6)) + log(3 x - 9) = log((3 x - 9)/(2 x + 6)):
log((3 x - 9)/(2 x + 6)) = 0

Cancel logarithms by taking exp of both sides:
(3 x - 9)/(2 x + 6) = 1

Multiply both sides by 2 x + 6:
3 x - 9 = 2 x + 6

Subtract 2 x - 9 from both sides:
Answer: |x = 15