Question

If 10^x.10^y.10^z = 10^5, then the average of x, y and z is .........

Answer 1

Answer :

Given,

10ˣ × 10ʸ × 10ᶻ = 10⁵

⇒ 10ˣ⁺ʸ⁺ᶻ = 10⁵

Comparing between the powers,

x + y + z = 5

Thus, the avearge of x, y, z is

(x + y + z)/3

= 5/3

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Answer 2

${10}^{x} \times {10}^{y} \times {10}^{z} = {10}^{5} \\ \\ {10}^{ x + y + z} = {10}^{5} \\ \\ x + y + z = 5 \: \: \: \: \: \: \: - - - 1equation$


Average = (x + y + z)/3


Putting the value of x + y + z from 1equation,

Average = 5/3


I hope this will help you

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