Question

What is the solution to the equation 9^(x − 2) = 27?

x = 2.5
x = 0.5
x = −0.5
x = 3.5

Answer 1

@jim_thompson5910

Answer 2

use base three for both sides

Answer 3

since \(27=3^3\) and \(9=3^2\) you can write it as \[3^{2(x-2)}=3^3\]

Answer 4

You need to take the log of both sides give you \[\log_{9}27=x-2\]
And then solve for x

Answer 5

now that the bases are the same, set \[2(x-3)=3\] and solve for \(x\)

Answer 6

i get D

Answer 7

yeah D

Answer 8

mistake in the distributive law there

Answer 9

\[2(x-2)=3\\
2x-4=3\] etc