Question Number 150641 by maged last updated on 14/Aug/21
$$\mathrm{1}+\sqrt{\mathrm{3}^{\mathrm{x}} }=\mathrm{2}^{\mathrm{x}} \\ $$$$\mathrm{x}=? \\ $$
Commented by amin96 last updated on 14/Aug/21
$$\sqrt{\mathrm{3}^{{x}} }=\mathrm{3}^{{m}} \:\:\:\:\mathrm{3}^{{x}} =\mathrm{3}^{\mathrm{2}{m}} \:\:\:{x}=\mathrm{2}{m} \\ $$$$\mathrm{1}+\mathrm{3}^{{m}} =\mathrm{4}^{{m}} \:\:\:\Rightarrow\:\:\:\mathrm{1}+\mathrm{3}=\mathrm{4}\:\:{m}=\mathrm{1} \\ $$$${x}=\mathrm{2} \\ $$
Answered by 7770 last updated on 14/Aug/21
$${x}=\mathrm{2} \\ $$
Answered by puissant last updated on 14/Aug/21
$${x}=\mathrm{2} \\ $$