THis is how I did it(or similar, this is from a few days ago, doing it now)
So we first convert all 25^whatevers into 5^somethings
so
5^-4 = 5^48/x OVER 5^26/x * 5*34/x = 5 ^(48-26-34)x = 5^-12x
so -12x = -4, x = 3
essentially the same as what you did
And also I'd nominate your answer for "Best Answer"