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If 2x = 4y = 8z and 1/(2x) + 1/(4y) + 1/(8z) = 4 , Find the Value of X. - Mathematics

Sum

If 2x = 4y = 8z and `1/(2x) + 1/(4y) + 1/(8z) = 4` , find the value of x.

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Solution

2x = 4y = 8z
⇒ 2x = 22y = 23x
⇒ x = 2y = 3z
⇒ y = `x/2 and z = x/3`

Now, `1/(2x) + 1/(4y) + 1/(8z) = 4`

⇒ `1/(2x) + 1/[(4y)/2] + 1/[(8z)/3] = 4`

⇒ `1/(2x) + 2/(4x) + 3/(8x) = 4`

⇒ `1/(2x) + 1/(2x) + 3/(8x) = 4` 

⇒ `[ 4 + 4 + 3 ]/(8x) = 4`

⇒ `11/(8x) = 4`

⇒ x = `11/32`

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 6 | Page 101
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