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2 years ago

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

Mathematics

2 answers:

weqwewe [10]2 years ago

4 0

9514 1404 393

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

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)

aksik [14]2 years ago

4 0

Answer:

Step-by-step explanation:

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

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