Question Number 206958 by hardmath last updated on 01/May/24
$$\mathrm{If}\:\:\:\frac{\mathrm{1}}{\mathrm{3}^{−\boldsymbol{\mathrm{x}}} }\:=\:\mathrm{5}\:\:\:\mathrm{find}:\:\:\mathrm{9}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:=\:? \\ $$
Answered by Frix last updated on 01/May/24
$$\mathrm{3}^{{x}} =\mathrm{5} \\ $$$$\left(\mathrm{3}^{{x}} \right)^{\mathrm{2}} =\mathrm{25} \\ $$$$\mathrm{9}^{{x}} =\mathrm{25} \\ $$$$\mathrm{9}×\mathrm{9}^{{x}} =\mathrm{225} \\ $$$$\mathrm{9}^{{x}+\mathrm{1}} =\mathrm{225} \\ $$
Commented by hardmath last updated on 01/May/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$
Commented by Frix last updated on 01/May/24
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Answered by MATHEMATICSAM last updated on 02/May/24
$$\frac{\mathrm{1}}{\mathrm{3}^{−\:{x}} }\:=\:\mathrm{5} \\ $$$$\Rightarrow\:\:\mathrm{3}^{{x}} \:=\:\mathrm{5} \\ $$$$\Rightarrow\:\left(\mathrm{3}^{{x}} \right)^{\mathrm{2}} \:=\:\mathrm{25} \\ $$$$\Rightarrow\:\mathrm{9}^{{x}} \:=\:\mathrm{25} \\ $$$$\Rightarrow\:\mathrm{9}^{{x}} \:×\:\mathrm{9}\:=\:\mathrm{225} \\ $$$$\Rightarrow\:\mathrm{9}^{{x}\:+\:\mathrm{1}} \:=\:\mathrm{225}\:\left(\mathrm{Ans}\right) \\ $$