If 2x = 3y = 12z ; Show that 1 Z = 1 Y + 2 X . - Mathematics

If 2^x = 3^y = 12^z ; show that `(1)/z = (1)/y + (2)/x`.

Sum

Let 2^x = 3^y = 12^z = k
⇒ `2 = "k"^(1/x), 3 = "k"^(1/y), 12 = "k"^(1/z)`
Now , 12 = 2 x 2 x 3

⇒ `"k"^(1/z) = "k"^(1/x) xx "k"^(1/x) xx "k"^(1/y)`

⇒ `(1)/z = (1)/x + (1)/x + (1)/y`

⇒ `(1)/z = (2)/x + (1)/y`.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
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