SOLUTION: solve for x and simplify 3a^(2x) + 3a^(-2x) = 10 where a>0 and a cannot equal 1

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for x and simplify 3a^(2x) + 3a^(-2x) = 10 where a>0 and a cannot equal 1      Log On


   

Question 1016459: solve for x and simplify
3a^(2x) + 3a^(-2x) = 10 where a>0 and a cannot equal 1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3a^(2x) + 3a^(-2x) = 10
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Multiply by a^(2x)
3a^(4x) + 3 = 10a^(2x)
3a^(4x) - 10a^(2x) + 3 = 0
Sub u for a^(2x)
3u^2 - 10u + 3 = 0
(3u - 1)*(u - 3) = 0
u = 1/3
a^(2x) = 1/3
2x*log(a) = log(1/3)
x = log(a)/log(1/9)
-----------------
a^(2x) = 3
x = log(a)/log(9)