If $5^x=6^y=30^7$, then what is the value of $\frac{1}{x}+\frac{1}{y}$?
Answer & explanation
Correct answer: option 2
$5^x=6^y=30^7$
$5^x=30^7$
⇒ 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) → $\frac{1}{7}$