SOLUTION: Use the substitution y=3^x to find the values of x which satisfy the equation
3^(2x+2)-10*3^(x) +1=0
I tried: 3^(2)*3^(x) + 3^(2) -10*3^(x) + 1 =0
Substituted in y: 9y +
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Question 936159: Use the substitution y=3^x to find the values of x which satisfy the equation
3^(2x+2)-10*3^(x) +1=0
I tried: 3^(2)*3^(x) + 3^(2) -10*3^(x) + 1 =0
Substituted in y: 9y + 9 - 10y + 1 = 0
which became: -y=-9 then y=9
so 3^x = 9 therefore x is 2 or so I thought.
The textbook answer given is -2 and 0.
Please could you help me and explain where I went wrong? Thank you.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Use the substitution y=3^x to find the values of x which satisfy the equation
3^(2x+2)-10*3^(x) +1=0
I tried: 3^(2)*3^(x) + 3^(2) -10*3^(x) + 1 =0
It's 3^2*3^(2x) -10*3^x + 1 = 0
--> 9y^2 - 10y + 1 = 0
======================================
You had the right idea, but having 2 answers should make you expect a quadratic.
--------------------------------------
Substituted in y: 9y + 9 - 10y + 1 = 0
which became: -y=-9 then y=9
so 3^x = 9 therefore x is 2 or so I thought.
The textbook answer given is -2 and 0.
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