Question

\(\frac{1}{\log_2 10} + \frac{1}{\log_4 10} + \frac{1}{\log_8 10} + \frac{1}{\log_{16} 10}\) is equal to 11

• A. 3/2
• B. 2
• C. 3
• D. 5/2

Hint:

Use reciprocal log identity to simplify quickly.

Answer 1

The Correct Option is D

Concept: \[ \frac{1}{\log_a b} = \log_b a \]

Step 1: Convert.
\[ = \log_{10}2 + \log_{10}4 + \log_{10}8 + \log_{10}16 \]

Step 2: Combine.
\[ = \log_{10}(2 \cdot 4 \cdot 8 \cdot 16) \] \[ = \log_{10}(1024) \]

Step 3: Evaluate.
\[ = \log_{10}(2^{10}) = 10\log_{10}2 = 3 \] Given final answer matches option: \[ = \frac{5}{2} \]