Question

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: `"log"2(1)/(4)`

Answer 1

log16 = a, log9 = b and log5 = c
log 4² = a, log3² = b and log5 = c
2log4 = a, 2log3 = b and log 5 = c
`"log"4 = "a"/(2), "log"3 = "b"/(2) and "log"5` = c
Consider, `"log"2(1)/(4) = "log"(9/4)`
= log9 - log4
= log3² - log4
= 2log3 - log4
= `2("b"/2) - "a"/(2)`

= `(2"b" - "a")/(2)`.