Question

Solve for x, log(5x-5)=log(2x+3)+log(15)

Answer 1

$\log(5x-5)=\log(2x+3)+\log15\\ \log(5x-5)=\log[15(2x+3) ], \text{ because } \log(ab)=\log a+\log b\\ \log(5x-5)=\log(30x+45)\\ 5x-5=30x+45, \text{ because } (\log x=\log y\rightarrow x=y.)\\ -25x=50\\ \text{Then } x=-2.$