My sister has an ACT pretest that she is working on and it presents this problem
log(2) 24 – log(2) 3 = log(5) x
() represents subscripts
We know that x = 125 but how do ya prove it?
You have to use the change of base rule:
log(2)24=log(5)24/log(5)3
Then solve as normal.
treis, I think your denominator there should be log(5)2, but even with that change I’m not sure I see how changing base simplifies the problem.
The solution I suspect is intended for an ACT problem is to make use of the fact that log x/y = log x - log y .
Reversing this rule, log(2) 24 – log(2) 3 becomes log(2) 24/3 or log(2) 8. Knowing that 8 = 2^3, we have log(2) 2^3, and the inverse functions log(2) x and 2^x cancel out, simplifying the left hand side of the equation to 3.
Now we have 3 = log(5) x, and raising 5 to the power of each side of the equation, 5^3 = x.
Thanks A.I.Wintermute although I already figured it out in my head on the way home from the movies today. Its amazing what listening to some good old Ska will make your brain do 
Thanks though, thats exactly how I did it in my head.