Question:
Given that \(113^{0.99} = x\), \(113^{0.77} = y\) and \(x^z = y^2\), then the value of z is close to:
यह देखते हुए कि \(113^{0.99} = x\), \(113^{0.77} = y\) और \(x^z = y^2\), तो z का मान करीब है:
Options :
- a) 3.04
- b) 1.56
- c) 1.48
- d) 2.89
- a) 3.04
- b) 1.56
- c) 1.48
- d) 2.89
correct answer : b)
Explanation :
x^z = (113^0.99)^z = 113^(0.99z).
y^2 = (113^0.77)^2 = 113^(1.54).
Equating powers: 0.99z = 1.54 ⇒ z = 1.54 / 0.99 = 1.555… ≈ 1.56.
x^z = (113^0.99)^z = 113^(0.99z).
y^2 = (113^0.77)^2 = 113^(1.54).
समान शक्तियाँ: 0.99z = 1.54 ⇒ z = 1.54 / 0.99 = 1.555… ≈ 1.56।