Question

if 2^x=5^y=10^-z, then what is the value of (1/x+1/y+1/z)


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Answer 1

Solution:

Given 2^x = 5^y = 10^-z

Let 2^x = 5^y = 10^-z = k

=> 2^x = k => 2 = k^1/x----(1)

=> 5^y = k => 5 = k^1/y ----(2)

=> 10^-z = k =>10 = k^-1/z--(3)

Now ,

From (3),

10 = k^-1/z

=> (2×5 ) = k^-1/z

=> k^1/x × k^1/y = k^-1/z

=> k^(1/x+1/y) = k^-1/z

=> 1/x + 1/y = -1/z

=> 1/x + 1/y + 1/z = 0

••••

Answer 2

Answer:

Please find the attached image.

Step-by-step explanation: