why did you take log(base25)?

take log(base5) of both sides:

log(base5)X = log(base5)25 ^ (1 + log(base 5) X)

call log(base5) just log, and remember we're working in base 5

=> logx = (1 + logx)log25

=> logx = (1 + logx)2 .................log(base5)25 = 2

=> logx = 2 + 2logx

=> logx = -2

=> 5^-2 = x

=> 1/5^2 = x

=> x = 1/25