Question

Plz solve this Equation?
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Answer 1

Given Equation

$\sf \to \: {4}^{x} \times {2}^{y} = 128$

$\sf \to \: {3}^{3x + 2y} = {9}^{xy}$

Now Take

$\sf \to \: {4}^{x} \times {2}^{y} = 128$

Using Exponential Properties

$\sf \to \: {2}^{2x} \times {2}^{y} = 128$

$\sf \to \: {2}^{2x + y} = 128$

$\sf \to \: {2}^{2x + y} = (2)^{7}$

We get

$\sf \to2x + y = 7$

Now Take

$\sf \to \: {3}^{3x + 2y} = {9}^{xy}$

$\sf \to \: {3}^{3x + 2y} = {3}^{2xy}$

We get

$\sf \to \: 3x + 2y = xy$

Answer

$\sf \to2x + y = 7$

$\sf \to \: 3x + 2y = xy$