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Question Number 202308 by 2024 last updated on 24/Dec/23

Commented by mr W last updated on 24/Dec/23

(4^x /9^x )=9  ((2/3))^(2x) =3^2   ((2/3))^x =3  xlog ((2/3))=log 3  ⇒x=((log 3)/(log 2−log 3))≈−2.7095

$$\frac{\mathrm{4}^{{x}} }{\mathrm{9}^{{x}} }=\mathrm{9} \\ $$$$\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}{x}} =\mathrm{3}^{\mathrm{2}} \\ $$$$\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{{x}} =\mathrm{3} \\ $$$${x}\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{3}}\right)=\mathrm{log}\:\mathrm{3} \\ $$$$\Rightarrow{x}=\frac{\mathrm{log}\:\mathrm{3}}{\mathrm{log}\:\mathrm{2}−\mathrm{log}\:\mathrm{3}}\approx−\mathrm{2}.\mathrm{7095} \\ $$

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