Question

Solve the equation
${2}^{x} \times {6}^{y} = 24 - - - - - - (1)$
${2}^{2x} \times {3}^{y } = 48 - - - - - - - (2)$
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Answer 1

Answer:

$2^x*6^y=24$

$2^x=\frac{24}{6^y}$

$2^{2x}*3^y=48$

$4*2^x*3^y=48$

Replacing $2^x$ with $\frac{24}{6^y}$

$4*\frac{24}{6^y}*3^y=48$

$\frac{4*24*3^y}{6^y} = 48$

$\frac{3^y}{6^y} =\frac{48}{4*24}$

$\frac{3^y}{2^y*3^y}=\frac{1}{2}$

$\frac{1}{2^y}=\frac{1}{2}$

$2^y=2$

$y=1$

$2^x*6^y=24$

$2^x*6=24$

$2^x=4$

$2^x=2^2$

Bases are same,

$x=2$

$x=2, y=1$