Question

if (2/3)^x * (3/2)^2x = 81/16 find x

Answer 1

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The value of x is 4  (EXPLANATION IS THERE IN THE ATTACHMENTS PLEASE REFER THEM AND MARK AS BRAINLIEST AND GIVE THANKS PLEASE)

Answer 2

Step-by-step explanation:

$given \: ( \frac{2}{3} )^{x} \times ( \frac{3}{2} )^{2x} = \frac{81}{16}$

$As,x ^{a} = \frac{1}{ {x - a}^{2} }$

$( \frac{3}{2} )^{ - x} \times ( \frac{3}{2} ) ^{2x} = \frac{81}{16}$

$As, \: {x}^{a} \times {x}^{b} = {x}^{a + b}$

$( \frac{3}{2} )^{ - x + 2x} = \frac{ 81}{16}$

$( \frac{3}{2} )^{ x } = \frac{ 81}{16}$

$( \frac{3}{2} ) ^{x} = ( \frac{3}{2} ) ^{4}$

comparing both the side

x = 4