To solve this logarithmic equation, we can rewrite it as an exponential equation.

Using the fact that log base a $x$ = y is equivalent to a^y = x, we can rewrite the equation as:

2^$-1$ = 3x - 5

1/2 = 3x - 5

Now, let's solve for x:

1/2 + 5 = 3x

5.5 = 3x

x = 5.5 / 3

x = 1.83

Therefore, the solution to the equation log base 1/2 of $3x-5$ = -1 is x = 1.83.