This one I believe is easier than it looks. First you want to start by isolating the part with the exponent. To do this start by dividing both sides by (1/4) and you get….
(5/6)^x= (25/36)
Immediately, it’s noticeable that 25 is 5^2 and 36 is 6^2
So you can rewrite this equation as
(5/6)^x=(5/6)^2
Because the bases are the same now, all you need to do is solve for the exponents. In which you get x=2.