log\(_{4\sqrt[3]{4^2}}\) \(\bigg(\frac{1}{1024}\bigg)\) is equal to(a)

1.	log\(_{4\sqrt[3]{4^2}}\) \(\bigg(\frac{1}{1024}\bigg)\) is equal to(a) – 5 (b) – 3 (c) 3 (d) 5
Answer» (b) - 3 Hint. Since \({4\sqrt[3]{4^2}}\) = 2².(2⁴)^{\(^{\frac{1}{3}}\)}= \(2^{2+\frac{4}{3}}\) = \(2^{\frac{10}{3}}\) and 1024 = 2¹⁰, therefore, log\(_{4.\sqrt[3]{4^2}}\) \(\bigg(\frac{1}{1024}\bigg)\) = log_2^10/3(2^-10) = \(\frac{-10}{\frac{10}{3}}\) log₂ 2 = – 3 × 1 = – 3. \(\bigg[\)Using log_ax^m= \(\frac{m}{n}\) log_a x\(\bigg].\)

log\(_{4\sqrt[3]{4^2}}\) \(\bigg(\frac{1}{1024}\bigg)\) is equal to(a) – 5 (b) – 3 (c) 3 (d) 5

Answer»

(b) - 3

Hint.

Since \({4\sqrt[3]{4^2}}\) = 2².(2⁴)^{\(^{\frac{1}{3}}\)}= \(2^{2+\frac{4}{3}}\) = \(2^{\frac{10}{3}}\) and

1024 = 2¹⁰, therefore,

log\(_{4.\sqrt[3]{4^2}}\) \(\bigg(\frac{1}{1024}\bigg)\) = log_2^10/3(2^-10) = \(\frac{-10}{\frac{10}{3}}\) log₂ 2

= – 3 × 1 = – 3. \(\bigg[\)Using log_ax^m= \(\frac{m}{n}\) log_a x\(\bigg].\)