SOLUTION: find x if x^log a base 2 + a^log x base 2 = 2a^2 (a>0)

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Question 970600: find x if x^log a base 2 + a^log x base 2 = 2a^2 (a>0)
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Given,
x%5E%28log%282%2Ca%29%29%2Ba%5E%28log%282%2Cx%29%29=2a%5E2
.
.
=> x^(log(x,a)/log(x,2))+a%5E%28log%282%2Cx%29%29=2a%5E2 (using %28log%28a%2Cb%29%29=%28%28log%28x%2Cb%29%29%2F%28log%28x%2Ca%29%29%29
.
=> a^(1/(log(x,2)))+a%5E%28log%282%2Cx%29%29=2a%5E2
=> a%5E%28log%282%2Cx%29%29%2Ba%5E%28log%282%2Cx%29%29=2a%5E2
=> 2a%5E%28log%282%2Cx%29%29=2a%5E2
Comparing exponents, we get,
%28log%282%2Cx%29%29=2
=> x=2%5E2
=> x=4