Question

What is the value of \( \log 8 / \log 64 \)?

• A. 0.25
• B. \( \frac{1}{3} \)
• C. 0.5
• D. None of these

Hint:

When working with logarithms, use the properties of exponents to simplify them and reduce the expression to a basic ratio.

Answer 1

The Correct Option is B

We know that: \[ \log_b a = \frac{\log a}{\log b} \] So, \[ \frac{\log 8}{\log 64} \] Since \( 8 = 2^3 \) and \( 64 = 2^6 \), we can rewrite the logarithms: \[ \frac{\log 2^3}{\log 2^6} = \frac{3 \log 2}{6 \log 2} = \frac{3}{6} = \frac{1}{3} \] Thus, the correct answer is \( \frac{1}{3} \).