Solve equation: 3^(3x) - 4 * 3^(2x) + 2 * 3x=8!

Question

basic concept 

Answer 1

3^3x - 4(3)^2x + 2(3^x) = 8

 

(3^x)³ - 4(3^x)² + 2(3^x) = 8

 

 

Let         q = 3^x

 

q³ - 4q² + 2q = 8

 

q³ - 4q² + 2q - 8 = 0

 

 

Factor by grouping.

 

q²(q - 4) + 2(q - 4) = 0

 

(q² + 2)(q - 4) = 0

 

q = 4         or          q = ±i√(2)

 

3^x = 4                

 

Use logarithms to solve for x.