Question

Solve the exponential equation. 2x = 1/2

Options: -1
-1/2
1

Answer 1

You meant exponential equation
is it 2^x = 1/2
if so

2^x = 1/2
2^x = 2^-1
   x = -1

answer
-1

Answer 2

It's very important that you use " ^ " to indicate exponentiation.

2x = 1/2 is an entirely different problem; its solution is x = 1/4.

You are to solve   2^x = 1/2.

                           1                           1
Note that 1/2 = --------,   so 1/2 = -------- = 2^x
                           2^1                     2^1

Multiplying both sides by 2, we get   1 = 2(2^x)   =  (2^1)(2^x) = 2^(x+1)

Take the log to the base 2 of both sides of     1 = 2^(x+1).  The result is

                                                                         0 = (x+1)(1), or 0 = x+1

Then x = -1.

check:      subst. -1 for x in   2^x = 1/2.  Is the equation then true?

2^(-1) = 1/2  ?

1
--  = 1/2?  Yes.  So, x=-1 has been verified.
2