Question

What is the solution to this equation? (1/27)2-x =9^3x

Answer 1

x = -2

Explanation:

Prime factorize, 27 and 9

27 = 3 *3 * 3 = 3³

9 = 3*3 = 3²

`\sf \left((1)/(27)\right)^(2-x)=9^(3x)\\\\`

`\left((1)/(3^3)\right)^(2-x)=9^(3x)\\\\(3^(-3))^(2-x)=(3^2)^(3x)\\\\3^((-3)*(2-x))=3^(2*3x)\\\\3^(-6+3x) = 3^(6x)`

Bases are same, so now compare the exponents

-6 + 3x = 6x

3x = 6x + 6

3x - 6x = 6

-3x = 6

x = 6/(-3)

`\sf \boxed{\bf x = -2}`

Exponent law:

`(x^m)^n=x^(m*n)\\\\\left((1)/(a^(m))\right)=a^(-m)\\`