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Question Number 149775 by mathdanisur last updated on 07/Aug/21

Solve the equation:  5^x  = (3^x  − 2^x )^2

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{5}^{\boldsymbol{\mathrm{x}}} \:=\:\left(\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \right)^{\mathrm{2}} \\ $$

Commented by amin96 last updated on 07/Aug/21

(9−4)^x =(3^x −2^x )^2 ⇒ (3^2 −2^2 )^x =(3^x −2^x )^2   x=2

$$\left(\mathrm{9}−\mathrm{4}\right)^{{x}} =\left(\mathrm{3}^{{x}} −\mathrm{2}^{{x}} \right)^{\mathrm{2}} \Rightarrow\:\left(\mathrm{3}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} \right)^{{x}} =\left(\mathrm{3}^{{x}} −\mathrm{2}^{{x}} \right)^{\mathrm{2}} \\ $$$${x}=\mathrm{2} \\ $$

Commented by mathdanisur last updated on 07/Aug/21

Thanks Ser

$$\mathrm{Thanks}\:\mathrm{S}{er} \\ $$

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