If 2^(2x-1) + 4^x = 2 ^(x-1/2) + 2^(x+1/2), then x =?
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2^(2x-1) + 4^x = 2^(x - 1/2 ) + 2^(x + 1/2)
2^2x /2 + 4^x = 2^x/√2 + 2^x.√2
4^x/2 + 4^x = 2^x{ 3/√2}
4^x(3/2) = 2^x(3/√2)
4^x = 2^x(√2)
2^2x =2^(x + 1/2)
2x = x + 1/2
x = 1/2
2^2x /2 + 4^x = 2^x/√2 + 2^x.√2
4^x/2 + 4^x = 2^x{ 3/√2}
4^x(3/2) = 2^x(3/√2)
4^x = 2^x(√2)
2^2x =2^(x + 1/2)
2x = x + 1/2
x = 1/2
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