Question

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 720

Answer 1

log16 = a, log9 = b and log5 = c
log4² = a, log3² = b and log5 = c
2log4 = a, 2log3 = b and log5 = c
`"log"4 = "a"/(2) , "log"3 = "b"/(2) and "log"5` = c
Consider, log720 = log(4² x 3² x 5)
= log4² + log3² + log5
= 2log4 + 2log3 + log5
= `2("a"/2) + 2 ("b"/2) + "c"`
= a + b + c.