Find all values of c such that

Question

3^(2c+1)=28*(3^c)-9. If you find more than one value of c, then list your values in increaing order, separated by commas.

Answer 1

3^(2c+1)=28*(3^c)-9
3^(2c)*3^1 = 28*3^c - 9
3(3^c)^2 - 28(3^c) + 9 = 0
let 3^c = x
3x^2 - 28x + 9 = 0
(3x - 1)(x - 9) = 0
x = 1/3 or x = 9

if x = 1/3
3^c= 1/3 = 3^-1 -----> c = -1

if x = 9
3^c = 9 = 3^2 ----> c = 2