Question

solve the following
(81)^-4÷(729)^2-x=9^4x​

Answer 1

the value of x is 1/7.

Hope it help .

Answer 2

Answer:

The value of x is -14.

Step-by-step explanation:

Given : 81⁻⁴ ÷ 729²⁻ˣ = 9⁴ˣ

This can be written as $\frac{81^{-4} }{729^{2-x} }$ = 9⁴ˣ

In order to solve this, we have to convert them to the same base.

We know that 9² = 81  and 9³ = 729. Therefore,

=> $\frac{(9^{2}) ^{-4} }{(9^{3})^{2-x} }$ = 9⁴ˣ

=> $\frac{9^{-8} }{9^{6-3x} }$ = 9⁴ˣ                  (because $(x^{n})^{m} = x^{nm}$ )

=> $9^{-8-(6-3x)}$ = 9⁴ˣ         (because $\frac{x^{n}}{x^{m}} = x^{n-m}$)

=>  $9^{-8-6+3x}$ = 9⁴ˣ

=> $9^{-14+3x}$ = 9⁴ˣ

As the base is same on both the left and right hand side, the exponents can be equated.

=> -14 + 3x = 4x

=> 3x - 4x = 14

=> -x = 14

=> x = -14

Therefore, the value of x is -14.