Find the value of x if \[9^x - 6\cdot 3^x - 55 = 0\]
Let 3^x = m
So
9^x - 6*3^x - 55 = 0
(3^2)^x - 6*3^x - 55 = 0
(3^x)^2 - 6* 3^x - 55 = 0
m^2 - 6m - 55 = 0
(m - 11) ( m + 5) = 0
Only the first factor set to 0 and solved for m gives us our answer
m - 11 = 0
m = 11
3^x = 11
x = log 11 / log 3
