Which of the following statement is true?

Engineering

Mathematics

Properties of Logarithm

Question

${log}_{\sec \frac{π}{3}} 0 . \bar{8} > 1$

$\log_{\sqrt{2}} (8) < \log_{\sqrt{3}} (9)$

2^1/2 < 3^1/3

log₄(3) < log₂₀(9)

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(1) log₄3 < 2 log₂₀3 ⇒ log₄3 < $\frac{2}{\log_{3} 20} \Rightarrow$ log₄20 < 2 ⇒ 2 < log₄20 < 3 ⇒ False.
(2) $\log_{2} 0. \bar{8}$ > 1   (False)
(3) $\log_{2^{1 / 2}} 2^{3} < \log_{3^{1 / 2}} 3^{2}$
       6 < 4    (False)
(4) $2^{1 / 2} < 3^{1 / 3}$
       2³ < 3²