What is the real value of x in the equation log(subscript 2)24-log(subscript 2)3=log(subscript 5)x?

Question

I really cannot remember at all how logs work. I know the answer is 125 but have no idea how to get there. Thanks in advance.

Answer 1

Two things to remember

1. log_a x = y is the same as a^y = x

2. Log A - Log B = Log (A/B) as long as the bases are the same

so log(subscript 2)24-log(subscript 2)3=log(subscript 5)x

log₂(24/3) = log₅ x
log₂8 = log₅ x
3 = log₅ x
5^3 = x
125 = x