If log 3=a, log 5=b and log 7=c, express log_{15} 7 in terms of a,b and c.

Answer 1

3 = 10^a
5 = 10^b

7 = 10^c

15 = 10^(a+b)

15^(log15 7) = 7 = [10^(a+b)]^log15 7

10^c = 10^(a+b)log15 7
so
c = (a+b) log15 7
log15 7 = c/(a+b)