Without using log, Solve for x. 27^(1-x) =(1)/(9^(2x) )

Question

Without using log, Solve for x.


`27^(1-x) =(1)/(9^(2x) )`

Answer 1

`x = - 3`

Step-by-step explanation

The given equation is

`27^(1-x) =(1)/(9^(2x) )`

Recall that

`\frac{1}{ {a}^(m) } = {a}^( - m)`

Apply this rule on the right hand side to get,

`27^(1-x) =9^( - 2x)`

Express both sides to base 3.

`3^(3(1-x)) =3^(2( - 2x))`

Equate the exponents:

3(1-x)=2(-2x)

Expand:

`3 - 3x = - 4x`

Group like terms,

`4x - 3x = - 3`

`x = - 3`