SOLUTION: This is supposed to be an exponential equation of quadratic type, but I'm just not seeing it: 2^x-10(2^-x) +3 = 0 Here's what I did: 2^x - 20^-x + 3 = 0 2^x - (20^-1)^x + 3 =

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Question 1103126: This is supposed to be an exponential equation of quadratic type, but I'm just not seeing it:
2^x-10(2^-x) +3 = 0
Here's what I did:
2^x - 20^-x + 3 = 0
2^x - (20^-1)^x + 3 = 0
2^x - (1/20)^x +3 = 0
2^x - (1^x/20^x) +3 = 0
And now I'm stumped. I really don't know what I'm doing here. Can you help? Thank you.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Your equation is

 = 0.


It is a quadratic equation (or EQUIVALENT to a quadratic equation) relative to the variable .


To see it CLEARLY, introduce new variable u = .


Then your equation takes the form

 = 0.


Multiply by u to rid off the denominator. You will get

 = 0,

 = 0.


Factor left side

(u+5)*(u-2) = 0


Only postive root works and make sense: u = 2.


It means  = u = 2,  which implies  x = 1.

Solved.

That's all.

Introducing new variable is the STANDARD method of solutions to problems like this.

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See the lesson
    - Solving exponential equations
in this site.


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