How do you solve (1/2)^x = log (base1/2) X?

Answer 1

This is a curiously interesting problem. If x = a^x, then Log((base a),x) = x. Thus we have a^x = Log((base a),x). So, the solution can be found by solving x = a^x. This involves the use of Lambert's W function, but for a = 1/2, the numerical approximation is 0.641185. That is:

0.641185 = (1/2)^(0.641185) = Log((base 1/2), 0.641185)

You get a star for bringing up this little curiosity.

Answer 2

Not sure what class you are taking, Lambert's W is one method.
but one way is to graph each side individually on a calculator and find the intersection
y1= (1/2)^x
y2= log(x)/log(1/2) using change of base

get x = .64118574

Answer 3

(1/2)^(1/2)^x = x