given-3-y-1-6-2-x-3-y-x-2-find-1-x-1-y-

Question Number 77186 by jagoll last updated on 04/Jan/20

given

{\begin{cases} 3^{y} - 1 = \frac{6}{2^{x}} \\ {(3)}^{\frac{y}{x}} = 2 \end{cases} find \frac{1}{x} + \frac{1}{y} .

Answered by john santu last updated on 04/Jan/20

\Rightarrow (3^{y}) = (2^{x})

l e t 2^{x} = j \Rightarrow j^{2} - j - 6 = 0

(j - 3) (j + 2) = 0 \Rightarrow {\begin{cases} j = 3 \Rightarrow x = \log_{2} (3) \\ 3^{y} = 3 \Rightarrow y = 1 \end{cases}

t h e r e f o r e \frac{1}{x} + \frac{1}{y} = \log_{3} (6)