If $ 60^{\dfrac{1}{a}} = 3$, $60^{\dfrac{1}{b}} = 10$ and $ 60^{\dfrac{1}{c}} = 120$.
Calculate \[ \dfrac{bc + ac + ab}{abc}\]
+128406 60^(1/a) = 3
Take the log of both sides
log 60^(1/a) = log 3
(1/a) log 60 = log 3
1/a = log 3 /log 60
Similarly (1/b) = log 10 / log 60
And (1/c) = log 120 / 60
(bc + ac + ab) / abc = 1/a + 1/b + 1/c =
log 3 / log 60 + log 10 / log 60 + log 120 /log 60 =
(log 3 + ;log 10 + log 120) / log 60 =
log (3* 10 * 120) / log 60 =
log(3600) / log (60) =
log 60^2 / log 60 =
2l log 60 / log 60 =
2
