Question

It is given that 2^x = 5^y = 10^z , express z in terms of x and y​

Answer 1

Step-by-step explanation:

Answer 2

9514 1404 393

Answer:

z = (xy)/(x+y)

Explanation:

Taking logarithms base 10, we have ...

x·log(2) = y·log(5) = z·log(10)

z = x·log(2) = y·log(5) . . . . . . . . log(10) = 1

__

Then z/x = log(2), and z/y = log(5), so ...

z/x +z/y = log(2) +log(5) = log(2·5) = 1

z = 1/(1/x +1/y) = 1/((x+y)/(xy))

z = (xy)/(x+y)