Question

answer 9^-2÷729^1-x=9^2x​

Answer 1

$\underline{\bold{Answer:}}$

$\text{Now},\: \dfrac{9^{-2}}{729^{(1-x)}} = 9^{2x}$

$\to \dfrac{9^{-2}}{9^{3*(1-x)}} = 9^{2x}$

$\to \dfrac{9^{-2}}{9^{(3-3x)}} = 9^{2x}$

$\to 9^{-2} * 9^{-(3-3x)} = 9^{2x}$

$\to 9^{-2-3+3x} = 9^{2x}$

$\to 9^{3x-5} = 9^{2x}$

$\small{\text{Comparing among the powers, we get}}$

$3x - 5 = 2x$

$\to 3x-2x = 5$

$\implies \boxed{\bold{x = 5}}$ ,

$\text{which is the required solution.}$