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
${\displaystyle \text{log}4=\frac{\text{a}}{2},\text{log}3=\frac{\text{b}}{2}\text{and}\text{log}5}$ = c
Consider, log720 = log(4² x 3² x 5)
= log4² + log3² + log5
= 2log4 + 2log3 + log5
= ${\displaystyle 2\left(\frac{\text{a}}{2}\right)+2\left(\frac{\text{b}}{2}\right)+\text{c}}$
= a + b + c.