log1/2(x-6)>-1

To solve the inequality log base 1/2 of (x-6) > -1, we can rewrite it in exponential form to eliminate the logarithm.

The logarithmic inequality log base a of b > c is equivalent to the exponential inequality a^c < b.

So, for our inequality log1/2(x-6) > -1, we rewrite it as:

1/2^(-1) < x-6

2 < x-6

x > 8

Therefore, the solution to the inequality log1/2(x-6) > -1 is x > 8.