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Question Number 55284 by Mikael_Marshall last updated on 20/Feb/19

$$5^{x-2}-5^x+5^{x+1}=505$$

Commented by Kunal12588 last updated on 20/Feb/19

$$\left(5^x\times 5^{-2}\right)-5^x+\left(5^x\times 5\right)=505$$$$5^x(5^{-2}-1+5)=505$$$$5^x\left(\frac{1-25+125}{25}\right)=505$$$$5^x=\frac{505}{101}\times 25=125=5^3$$$$x=3$$

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