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Question Number 187381 by a.lgnaoui last updated on 16/Feb/23

$$3^x=5^y=225$$$$Determiner:\frac{1}{x}+\frac{1}{y}?$$

Answered by horsebrand11 last updated on 16/Feb/23

$$\{\begin{array}{l}x=\log {}_{3}225\\ y=\log {}_{5}225\end{array}\Rightarrow \frac{1}{x}+\frac{1}{y}=\log {}_{{15}^2}\left(15\right)=\frac{1}{2}$$

Commented by a.lgnaoui last updated on 16/Feb/23

$$thanks$$

Answered by anurup last updated on 17/Feb/23

$$3={225}^{\frac{1}{x}}5={225}^{\frac{1}{y}}$$$$\therefore 3\times 5={225}^{(\frac{1}{x}+\frac{1}{y})}$$$$\Rightarrow 15={15}^{2(\frac{1}{x}+\frac{1}{y})}$$$$\Rightarrow 2(\frac{1}{x}+\frac{1}{y})=1$$$$\Rightarrow \frac{1}{x}+\frac{1}{y}=\frac{1}{2}$$$$\mathrm{can}\mathrm{also}\mathrm{be}\mathrm{done}\mathrm{without}\mathrm{taking}\log$$

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