Mathematics - Quadratic Equation Question with Solution | TestHub

$\begin{array}{rl}& (8{)}^{2x}-16\cdot (8{)}^x+48=0\\ & \text{ Put }{8}^{\mathrm{x}}=\mathrm{t}\\ & {\mathrm{t}}^2-16+48=0\\ & \Rightarrow \mathrm{t}=4\text{ or }\mathrm{t}=12\\ & \Rightarrow 8^x=48^x=12\\ & \Rightarrow \mathrm{x}={\log }_8\mathrm{x}\mathrm{x}={\log }_{8}12\\ & \end{array}$ sum of solution $={\log }_{8}4+{\log }_{8}12$ $\begin{array}{rl}& ={\log }_{8}48={\log }_8(6.8)\\ & =1+{\log }_{8}6\end{array}$