Question

If (2^x ) ( 2^y) = 16 and (9^x )( 3^y) = 243 then find ( x , y) using linear equation concepts
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Answer 1

$\textbf{Given:}$

$\mathrm{2^x\,2^y=16}$

$\mathrm{9^x\,3^y=243}$

$\textbf{To find:}$

$\text{The value of x and y}$

$\textbf{Solution:}$

$\text{Consider,}$

$\mathrm{2^x\,2^y=16}$

$\mathrm{2^{x+y}=2^4}$

$\implies\mathrm{x+y=4}$......(1)

$\mathrm{9^x\,3^y=243}$

$\mathrm{3^{2x}\,3^y=3^5}$

$\mathrm{3^{2x+y}=3^5}$

$\implies\mathrm{2x+y=5}$.......(2)

$\mathrm{(2)-(1)\implies}$

$\boxed{\mathrm{x=1}}$

$\text{Put x=1 in (1)}$

$\mathrm{1+y=4}$

$\implies\boxed{\mathrm{y=3}}$

$\textbf{Answer:}$

$\text{(x,y)=(1,3)}$

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