3^2x-6*3^x+9=0

Question

help please

Answer 1

Let u = 3^x; now rewrite the given equation as u²-6u+9 = 0 which you should realize is a perfect square.

 

(u-3)² = 0  Therefore u = 3.  This means that 3^x = 3, so x = 1.

Answer 2

3^2x - 6(3^x) + 9 = 0

 

Note there is a quadratic equation disguised here.

 

(3^x)² - 6(3^x) + 9 = 0

 

Let y = 3^x

Then the equation becomes

 

y² - 6y + 9 = 0

 

(y - 3)² = 0

 

y = 3

 

3^x = 3

 

x = 1