\[\large 3^a=5^b=15\]
If \(a\) and \(b\) are numbers satisfying the equation above, find \(\dfrac{1}{a}+\dfrac{1}{b}\).
a = log 15 / log 3
b = log 15 / log 5
So
1/ ( log 15 / log 3) + 1 / ( log 15 . log 5) =
log 3 / log 15 + log 5 / log 15 =
(log 3 + log 5) / log 15 using a log property
log (3 * 5 ) / log 15
log 15 / log 15 =
1
