You can solve this problem by inspection or by plotting.
x^2 = 16^x
x^2 = 2^(4x)
x = 2^(2x)
Take log of both sides:
logx = 2xlog2
(logx)/x = 2log2
x^(1/x) = 2^2
x^(1/x) = 4
Plot problem:
x = -.5
Test (-.5)^(1/-.5) = 4, 4 =4
(-.5)^2 = 16^(-.5)
1/4 = 1/4
Answer is: -.5
