If logx 27 +logy 4 =5 and log x 27 -logy 4=1 find x and y

asked Jan 17, 2024 52.2k views

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Answer:

$(x,y)\rightarrow(3,2)$

Explanation:

I assume you mean
$\log_x(27)+\log_y(4)=5$ and
$\log_x(27)-\log_y(4)=1$ :

$\biggr(\log_x(27)+\log_y(4)\biggr)-\biggr(\log_x(27)-\log_y(4)\biggr)=5-1$

$2\log_y(4)=4\\\log_y(4)=2\\4=y^2\\2=y$

$\log_x(27)+\log_y(4)=5\\\log_x(27)+\log_2(4)=5\\\log_x(27)+2=5\\\log_x(27)=3\\27=x^3\\3=x$

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