log(base5)x+log(base25)x+log(base125)x=33

solve for x

2 answers

let's establish a property

let log(base25) x = y
25^y = x
5^(2y) = x
back to log notation ...
log(base5)x = 2y
y = (1/2)log(base5) x

so log(base5)x+log(base25)x+log(base125)x=33
log(base5)x + (1/2)log(base5)x + (1/3)log(base5)x = 33
(11/6)log(base5)x = 33
log(base5)x = 18
x = 5^18
log base100 power1