If $5^x=6^y=30^7$, then what is the value of $\frac{1}{x}+\frac{1}{y}$?

$\frac{1}{7}$

$5^x=6^y=30^7$

$5^x=30^7$

⇒ 5^(x*1/x) =30^(7*1/x)

⇒ 5 =30^(7*1/x)

$6^y=30^7$ .......(1)

⇒ 6^(y*1/y) =30^(7*1/y)

⇒ 6 =30^(7*1/y) ............(2)

Multiply 1 and 2,

30 = (30^7*1/x) (30^7*1/y) = 30^7(1/x + 1/y)

⇒ 7(\(\frac{1}{x}\) + \(\frac{1}{y}\)) = 1

(\(\frac{1}{x}\) + \(\frac{1}{y}\)) = $\frac{1}{7}$ 

The correct answer is Option (2) → $\frac{1}{7}$