Question

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

Answer 1

Answer:

x = -8

Step-by-step 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

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