Question Number 45225 by mondodotto@gmail.com last updated on 10/Oct/18
$$\mathrm{solve}\:\mathrm{for}\:{x} \\ $$$$\mathrm{9}^{{x}+\mathrm{1}} +\mathrm{3}^{\mathrm{2}{x}+\mathrm{1}} =\mathrm{36} \\ $$
Answered by malwaan last updated on 10/Oct/18
$$\mathrm{9}.\mathrm{9}^{\mathrm{x}} +\mathrm{3}.\mathrm{9}^{\mathrm{x}} =\mathrm{36} \\ $$$$\mathrm{3}.\mathrm{9}^{\mathrm{x}} +\mathrm{9}^{\mathrm{x}} =\mathrm{12} \\ $$$$\mathrm{4}.\mathrm{9}^{\mathrm{x}} =\mathrm{12} \\ $$$$\mathrm{9}^{\mathrm{x}} =\mathrm{3} \\ $$$$\mathrm{3}^{\mathrm{2x}} =\mathrm{3}^{\mathrm{1}} \\ $$$$\Rightarrow\mathrm{2x}=\mathrm{1} \\ $$$$\mathrm{x}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by mondodotto@gmail.com last updated on 10/Oct/18
$$\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot} \\ $$