Solve for x. Please show your work.

log₂24-log₂3=log₅x     using a log rule, we can write

log₂ [ 24/3]  = log₅x

log₂ [8]  = log₅x

3  = log₅x

This says that, in exponential form,

5^3  = x   =  125

Solve for x:
(log(24))/(log(2))-(log(3))/(log(2)) = (log(x))/(log(5))

(log(24))/(log(2))-(log(3))/(log(2)) = (log(x))/(log(5)) is equivalent to (log(x))/(log(5)) = (log(24))/(log(2))-(log(3))/(log(2)):
(log(x))/(log(5)) = (log(24))/(log(2))-(log(3))/(log(2))

Multiply both sides by log(5):
log(x) = (log(5) log(24))/(log(2))-(log(3) log(5))/(log(2))

Cancel logarithms by taking exp of both sides:
Answer: | x = e^((log(5) log(24))/(log(2))-(log(3) log(5))/(log(2)))

                x=125