Solving 9^x - 5·3^x + 6 = 0

[EternityMech]

Homework Statement

9^x-5*3^X+6=0

Homework Equations

I have no idea how to solve this i suspect there is a theory that I am not familiar with involved.
want real numbers.

The Attempt at a Solution

i thought about moving the 6 to the otherside and doing log on both but you can't have ln(-6)
im clueless. need help thanks.

 

[HallsofIvy]

9= 3² so 9^x= (3²)^x= (3^x)².

Let y= 3^x and your equation becomes y²- 5y+ 6= 0, and easily factored quadratic. Once you know y, solve 3^x= y.