Find-the-value-of-x-from-the-following-equations-4-x-y-y-x-32-log-3-x-y-log-3-x-y-1-

Question Number 193295 by MATHEMATICSAM last updated on 09/Jun/23

Find the value of x from the following

equations :

4^{\frac{x}{y} + \frac{y}{x}} = 32

\log_{3} (x - y) + \log_{3} (x + y) = 1

Answered by BaliramKumar last updated on 09/Jun/23

2

Answered by Frix last updated on 09/Jun/23

x = p y

4^{p + \frac{1}{p}} = 4^{\frac{5}{2}} \Rightarrow p = \frac{1}{2} \lor p = 2

x - y > 0 \Rightarrow p > 1 \Rightarrow p = 2

\log_{3} (y) + \log_{3} (3 y) = 1

{2 \log}_{3} y + 1 = 1 \Rightarrow y = 1 \Rightarrow x = 2

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