Solve for $ x: 81^{-2} \div 729^{1-x}=9^{2 x} $
a) 2
b) -2

c) 7

d)-7

Given:   $ x: 81^{-2} \div 729^{1-x}=9^{2 x} $

To do:  Solve the expression.

Solution:

$81 = 9^2$

$729 = 9^3$

LHS= $81^-2 ÷ 729^{1-x} $

=$(9^2  )^-2 ÷ (9^3)^{1-x}$

= $9^-4 ÷ 9^{3-3x}$ 

$9^{-4+3x-3}$

RHS = $9^{2x}$

Comparing LHS and RHS

$3x - 7 = 2x$

$3x - 2x = 7$

$x = 7$

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Updated on: 10-Oct-2022

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