Question Number 174440 by mathlove last updated on 01/Aug/22
$$\mathrm{1}+\sqrt{\mathrm{3}^{{x}} }=\mathrm{2}^{{x}} \:\:\:\:\:\:\:\:{x}=? \\ $$
Commented by infinityaction last updated on 01/Aug/22
$$\mathrm{2} \\ $$
Commented by mathlove last updated on 01/Aug/22
$${solution}?? \\ $$
Commented by MJS_new last updated on 02/Aug/22
$$\mathrm{no}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{method}.\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{use} \\ $$$$\mathrm{your}\:\mathrm{experience}.\:\mathrm{3}^{\mathrm{2}} =\mathrm{9};\:\sqrt{\mathrm{9}}=\mathrm{3};\:\mathrm{3}+\mathrm{1}=\mathrm{4}=\mathrm{2}^{\mathrm{2}} \\ $$$$\mathrm{but}\:\mathrm{here}\:\mathrm{you}\:\mathrm{have}\:\mathrm{to}\:\mathrm{approximate}:\mathrm{1}+\sqrt{\mathrm{5}^{{x}} }=\mathrm{3}^{{x}} \\ $$