SOLUTION: If 10^x+10^-x=4. Prove that log base 10( 2+(3^1/2))= x

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Question 976054: If 10^x+10^-x=4. Prove that log base 10( 2+(3^1/2))= x
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Use the fact that 10^log10(x) = x, and substitute the given value for x:
Does 10^log10(2+sqrt(3)) + 1/10^log10(2+sqrt(3)) = 4 ?
Simplify the LHS:
2+sqrt(3) + 1/(2+sqrt(3)) = ((2+sqrt(3)(2+sqrt(3)) + 1)/(2+sqrt(3))
(4 + 4sqrt(3) + 3 + 1)/(2+sqrt(3)) -> (8+4sqrt(3))/(2+sqrt(3)) = 4(2+sqrt(3))/(2+sqrt(3)) = 4
Done