cat 2019 Question 29

Question

Let x and y be positive real numbers such that $\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3,$ and $\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$. Then $xy$ equals

Accepted Answer

We have, $\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3$

=> $x^2-y^2=125$......(1)

$\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$

=>$\ \frac{\ y}{x}$ = $\ \frac{\ 2}{3}$

=> 2x=3y => x=$\ \frac{\ 3y}{2}$

On substituting the value of x in 1, we get

$\ \frac{\ 5x^2}{4}$=125

=>y=10, x=15

Hence xy=150

Question 29.

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Question 29.

Question Explanation

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