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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-> 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(52777) (Show Source):
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.
