[tex]5*3^{x} = 3*5^{x}[/tex]
[tex]\ln \left(5\cdot \:3^x\right)=\ln \left(3\cdot \:5^x\right)[/tex][tex]\ln \left(5\right)+x\ln \left(3\right)=\ln \left(3\right)+x\ln \left(5\right)[/tex][tex]x\ln \left(3\right)-\ln \left(5\right)x=\ln \left(\frac{3}{5}\right)[/tex][tex]\frac{\left(\ln \left(3\right)-\ln \left(5\right)\right)x}{\ln \left(3\right)-\ln \left(5\right)}=\frac{\ln \left(\frac{3}{5}\right)}{\ln \left(3\right)-\ln \left(5\right)}[/tex][tex]x=-\frac{\ln \left(\frac{3}{5}\right)}{\ln \left(\frac{5}{3}\right)}[/tex]
