a) [latex]8^{3x-5}cdot4^{x-2}=2: sqrt[3]{16}[/latex] [latex](2^3)^{3x-5}cdot(2^2)^{x-2}=2:16^{frac{1}{3}}[/latex] [latex]2^{3(3x-5)}cdot2^{2(x-2)}=2:(2^4)^{frac{1}{3}}[/latex] [latex]2^{9x-15}cdot2^{2x-4}=2:2^{frac{4}{3}}[/latex] [latex]2^{9x-15+2x-4}=2^{-frac{1}{3}}[/latex] [latex]2^{11x-19}=2^{-frac{1}{3}}[/latex] [latex]11x-19=-frac{1}{3} / cdot 3[/latex] [latex]33x-57=-1[/latex] [latex]33x=-1+57[/latex] [latex]33x=56 /:33[/latex] [latex]x= frac{56}{33}[/latex] [latex]x=1 frac{23}{33}[/latex] b) [latex]7cdot27^{x-2}=frac{7}{81} /:7[/latex] [latex]27^{x-2}=frac{1}{81}[/latex] [latex](3^3)^{x-2}=frac{1}{3^4}[/latex] [latex]3^{3(x-2)}=3^{-4}[/latex] [latex]3(x-2)=-4[/latex] [latex]3x-6=-4[/latex] [latex]3x=-4+6[/latex] [latex]3x=2 /:3[/latex] [latex]x=frac{2}{3}[/latex]
