Question Number 109888 by bagusadisaputra last updated on 26/Aug/20
$$\mathrm{2}^{{x}+\mathrm{5}} =\sqrt{\mathrm{8}^{{x}} } \\ $$
Answered by som(math1967) last updated on 26/Aug/20
$$\mathrm{2}^{\mathrm{x}+\mathrm{5}} =\left(\mathrm{2}^{\mathrm{3x}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\mathrm{2}^{\mathrm{x}+\mathrm{5}} =\mathrm{2}^{\frac{\mathrm{3x}}{\mathrm{2}}} \\ $$$$\mathrm{x}+\mathrm{5}=\frac{\mathrm{3x}}{\mathrm{2}} \\ $$$$\mathrm{2x}+\mathrm{10}=\mathrm{3x} \\ $$$$\therefore\mathrm{x}=\mathrm{10}\:\mathrm{ans} \\ $$
Answered by Rasheed.Sindhi last updated on 26/Aug/20
$$\mathrm{AnOther}\:\mathrm{way}\circlearrowleft \\ $$$$\mathrm{2}^{{x}+\mathrm{5}} =\sqrt{\mathrm{8}^{{x}} } \\ $$$$\mathrm{2}=\mathrm{8}^{\mathrm{1}/\mathrm{3}} \\ $$$$\mathrm{8}^{\frac{{x}+\mathrm{5}}{\mathrm{3}}} =\mathrm{8}^{\frac{{x}}{\mathrm{2}}} \\ $$$$\frac{{x}+\mathrm{5}}{\mathrm{3}}=\frac{{x}}{\mathrm{2}} \\ $$$$\mathrm{2}{x}+\mathrm{10}=\mathrm{3}{x} \\ $$$${x}=\mathrm{10} \\ $$
Answered by Dwaipayan Shikari last updated on 26/Aug/20
$$\left({x}+\mathrm{5}\right){log}\left(\mathrm{2}\right)=\frac{\mathrm{3}{x}}{\mathrm{2}}{log}\mathrm{2} \\ $$$${x}=\mathrm{10} \\ $$