If 2400 = 2x X 3y X 5z, Find the Numerical Value of X, Y, Z. Find the Value of 2-x X 3y X 5z as Fraction.

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

Sum

2400 = 2^x x 3^y x 5^z
2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
∴ 2^x x 3^y x 5^z= 2⁵ x 3¹ x 5²
⇒ x = 5, y = 1, z = 2
∴ 2^-x x 3^y x 5^z = 2^-5 x 3¹ x 5²

= `(1)/(32) xx 3 xx 25`

= `(75)/(32)`.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 20

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2^{x + 3} + 2^{x + 1} = 320

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