Question

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

Answer 1

(3^2)^(x-2) = 3^3 ->

2(x-2) = 3 -> x = 7/2 (check 9^7/2-2 = 9^3/2 = 27)

Answer 2

I'm sorry I got confused, I thought lna/lnb=ln(a-b).
\[...x=\ln27/\ln9+2\]\[x=\ln3^3/\ln3^2+2\]\[x=3\ln3/2\ln3+2\]\[x=3/2+2\]\[x=7/2\]