Logarithm question

Question

Given: log 5=a, log 3=b and log 2=c, find log₃₀8

Answer 1

From change of base formula we can change log₃₀8 to base 10 by doing (log8)/(log30) since the other logs are given in base ten. Then we can factor 8 and 30 in terms of 5, 3, 2. Then we have log8 = log (2^3) = 3log2 since there is another log property where we can bring down the exponent to the front. So log8 = 3c. Then factoring 30 we have log(30) = log(5*3*2) = log5+log3+log2 by another log property that if you multiply inside the log it is the same as adding those factors in separate logs in the same base. So log(30) = a+b+c. Since we did change of base we have 3c/(a+b+c).

Hope that helped!