Question

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 75

Answer 1

log16 = a, log9 = b and log5 = c
log4² = a, log 3² = b and log5 = c
2log4 = a, 2log3 = b and log5 = c
`"log"4 = "a"/(2), "log"3 = "b"/(2) and log5` = c
Consider, log75 = log(5² x 3)
= log5² + log3
= 2log5 + log3
= `2("c") + "b"/(2)`

= `(4"c" + "b")/(2)`.