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Answer:
z = (xy)/(x+y)
Step-by-step 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
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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)
