Answer:
x = -8
Step-by-step explanation:
Given the equation:
[tex]27^x=9^{x-4}[/tex]
Note that
[tex]27=3^3\\ \\9=3^2,[/tex]
then
[tex]27^x=(3^3)^x=3^{3x}\\ \\9^{x-4}=(3^2)^{x-4}=3^{2(x-4)}[/tex]
Rewrite the equation as
[tex]3^{3x}=3^{2(x-4)},[/tex]
then
[tex]3x=2(x-4)\\ \\3x=2x-8\\ \\3x-2x=-8\\ \\x=-8[/tex]