Question 894613


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.