SOLUTION: 4^x + 4^-x = 5/2. What is x

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 Click here to see ALL problems on Trigonometry-basics Question 76373: 4^x + 4^-x = 5/2. What is xAnswer by ankor@dixie-net.com(15746)   (Show Source): You can put this solution on YOUR website!4^x + 4^-x = 5/2. What is x : Here is one approach: 4^-x is the reciprocal of 4^x : We can present the problem as "What number + it's reciprocal = 5/2?" : Let a = 4^x and write the problem: a + 1/a = 5/2 : a^2 + 1 = 5a/2; multiplied equation by a 2a^2 + 2 = 5a; multiplied equation by 2 2a^2 - 5a + 2 = 0; a quadratic equation (2a - 1)(a - 2) = 0; factored 2a = +1 a = 1/2 and a = +2 : use the last solution: 4^x = a 4^x = 2 We know 2 is the sqrt of 4 therefore x = 1/2 : Check: 4^1/2 + 4^(-1/2) = 2 + (1/2) = 5/2 : You can check and see if the other solution a = 1/2 will work. 4^x = (1/2) Use natural logs for this: x*ln(4) = ln(1/2) 1.38629x = -.693147 x = -.693147/1.38629 x = -.500000 or -1/2 : That makes the problem 4^(-1/2) + 4^-(-1/2) = 5/2 : Hope this round about way was some help to you.