3-x-5-y-225-Determiner-1-x-1-y-

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

3^{x} = 5^{y} = 225

D e t e r m i n e r : \frac{1}{x} + \frac{1}{y} ?

Answered by horsebrand11 last updated on 16/Feb/23

{\begin{cases} x = \log_{3} 225 \\ y = \log_{5} 225 \end{cases} \Rightarrow \frac{1}{x} + \frac{1}{y} = \log_{15^{2}} (15) = \frac{1}{2}

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

t h a n k s

Answered by anurup last updated on 17/Feb/23

3 = 225^{\frac{1}{x}} 5 = 225^{\frac{1}{y}}

∴ 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}

can also be done without taking \log

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