Solve log(5x-1) = 2 + log(x-2)

log(5x-1) = 2 + log(x-2)
log(5x-1) - log(x-2) = 2
log ( (5x-1)/(x-2) ) = 2
(5x-1)/(x-2) = 10^2 = 100

100x - 200 = 5x-1
95x = 199
x = 199/95

How did you arrive at 10^2?

By the definition of logs

log_a b = c <------> a^c = b

so if log₁₀( (5x-1)/(x-2) ) = 2 , then
10^2 = ( (5x-1)/(x-2) )