SOLUTION: 1. Solve the following equations a) 9^(x)- 5(3^x) +6 =0 (hint let y = 3^x) Can you please help me out? Thanks so much in advance:) Can you please show all the steps it would

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. Solve the following equations a) 9^(x)- 5(3^x) +6 =0 (hint let y = 3^x) Can you please help me out? Thanks so much in advance:) Can you please show all the steps it would       Log On


   

Question 744700: 1. Solve the following equations
a) 9^(x)- 5(3^x) +6 =0 (hint let y = 3^x)
Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
9^(x)- 5(3^x) +6 =0 (hint let y = 3^x)
%283%5E2%29%5Ex-5%283%5Ex%29%2B6=0
%283%5Ex%29%5E2-5%283%5Ex%29%2B6=0, There is a rule of exponents for that.
Your hinted substitution:
y%5E2-5y%2B6=0, which is factorable into....
%28y-2%29%28y-3%29=0

Either y=2 OR y=3
Reversing the substitution done,
Either 3%5Ex=2 Or 3%5Ex=3

Whatever base you want, find logarithms of both sides for each choice of solution.
log%283%5Ex%29=log%282%29
x%2Alog%283%29=log%282%29
highlight%28x=log%282%29-log%283%29%29, I skipped a step. You might want that as highlight%28x=%28log%282%29%29%2F%28log%283%29%29%29

Do similarly for the other choice.