Question

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 2.25

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, log2.25 = `"log"(225/100)`
= log225 - log100
= log(3² x 5²) - log(4 x 5²)
= log3² + log5² - (log4 + log5²)
= log3² + log5² - log4 - log5²
= 2log3 - log4
= `2("b"/2) - "a"/(2)`

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