Question

$log_{3} (x+2) + log_{3} (3x+6) = 5$

Answer 1

$\mathrm{\ell og}_{3\,}(x+2)+\mathrm{\ell og}_{3\,}(3x+6)=5\\ \\ \mathrm{\ell og}_{3\,}(x+2)+\mathrm{\ell og}_{3\,}[3\cdot (x+2)]=5\\ \\ \mathrm{\ell og}_{3\,}(x+2)+\mathrm{\ell og}_{3\,}(3)+\mathrm{\ell og}_{3\,}(x+2)=5\\ \\ 2\,\mathrm{\ell og}_{3\,}(x+2)+1=5\\ \\ 2\,\mathrm{\ell og}_{3\,}(x+2)=5-1\\ \\ 2\,\mathrm{\ell og}_{3\,}(x+2)=4\\ \\ \mathrm{\ell og}_{3\,}(x+2)=\frac{4}{2}\\ \\ \mathrm{\ell og}_{3\,}(x+2)=2\\ \\ x+2=3^{2}\\ \\ x+2=9\\ \\ x=9-2\\ \\ \boxed{\begin{array}{c}x=7 \end{array}}$