Question

27^x = 9^x − 4 Question 1 options: x = 8 x = 4 x = −4 x = −8

Answer 1

x = -8

Explanation:

Given the equation:

`27^x=9^(x-4)`

Note that

`27=3^3\\ \\9=3^2,`

then

`27^x=(3^3)^x=3^(3x)\\ \\9^(x-4)=(3^2)^(x-4)=3^(2(x-4))`

Rewrite the equation as

`3^(3x)=3^(2(x-4)),`

then

`3x=2(x-4)\\ \\3x=2x-8\\ \\3x-2x=-8\\ \\x=-8`