Question

Which of the following when simplified, vanishes

• A. $\frac{1}{\log_3 2} + \frac{2}{\log_9 4} - \frac{3}{\log_{27} 8}$
• B. $\log_2 (\frac{2}{3}) + \log_4 (\frac{9}{4})$
• C. – $\log_8 \log_4 \log_2 16$
• D. $\log_{10} \cot 1^\circ + \log_{10} \cot 2^\circ + \log_{10} \cot 3^\circ + \dots + \log_{10} \cot 89^\circ$

Answer 1

Answer: (A), (B), (C), (D)

A, B, C, D

Answer 2

Option (A) simplifies to 0 using logarithm properties. Option (B) simplifies to 0 using logarithm properties. Option (C) simplifies to 0 by direct evaluation of logarithms. Option (D) simplifies to 0 using logarithm and trigonometric identities.