if 5 to the power x = 6 to the power y = 30 to the power 7,then ((x*y)/(x+y)) equals how much?please explain?

Question

please do explain in detailed steps or logics.

Answer 1

5^x = 6^y = 30^7
xln(5) = yln(6) = 7ln(30)
x = 7ln(30) / ln(5)
y = 7ln(30) / ln(6)
x*y/(x + y) =
1/(1/x + 1/y) =
1/(ln(5) / 7ln(30) + ln(6) / 7ln(30)) =
1/(ln(30) / 7ln(30)) =
x*y/(x + y) = 7

Answer 2

the answer is 7

5^x = 6 ^y = 30^7

5^x = 30^7
taking log on both sides

xlg5 = 7lg30

x = 7lg30 / lg5

6^y = 30 ^7
taking lg on both sides

ylg6 = 7lg30

y = 7lg30/lg6

now simply throw in the numbers in (x*y) / (x+y)

the ans is 7

Answer 3

5^x = 6^y = 30^7
xln5 = yln6 = 7ln30
(x*y)/(x+y))
= [1/x + 1/y]^-1
= [ln5/(7ln30) + ln6/(7ln30) ]^-1
= [ln30/(7ln30)]^-1
= 7