SOLUTION: if log5 3 = a; and log3 4 = b then what is log12 75 in a and b

Question 894613: if log5 3 = a; and log3 4 = b
then what is log12 75 in a and b

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

terminology:

log(5,3) equals log 3 to the base of 5
log(3,4) equals log 4 to the base of 3
log(12,75) equals log 75 to the base of 12

since 12 equals 3*4, then log(12,75) is equivalent to log(3*4,75)

by the properties of logarithms, we get:

log(5,3) = a if and only if 5^a = 3, and we get:

log(3,4) = b if and only if 3^b = 4

we can now substitute in log(3*4,75) to get:

log(5^a*3^b,75)

this means log of 75 to the base of 5^a*3^b.

your solution is that log of 75 to the base of 12 is equivalent to log of 75 to the base of 5^a * 3^b.

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