Question 130714
I am not sure which way to read this problem.   I will work it both ways.

If it is 7^x-2/6=sqrt7
change sqrt7 to 7^1/2
equate the two exponents   x-2/6=1/2
 solve for x       x=1/2+2/6  get commom denominator
x=3/6+2/6
x=5/6

or if the problem is 

7^(x-2)/6=7^1/2
equate exponents and solve the equation for x

(x-2)/6=1/2   This is a proportion, so cross multiply.
2x-4=6
2x=10
x=5