Logarithms
View Questions of Logarithms
Quantitative Aptitude - Logarithms
1. Definition
Logarithm: \( \log_b(a) = c \equiv b^c = a. \)
2. Log Laws
- \( \log_b(mn) = \log_b(m) + \log_b(n) \)
- \( \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) \)
- \( \log_b(m^k) = k \log_b(m) \)
- Change of base: \( \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \)
3. Applications
- Solve exponential equations using logs.
- Apply in CI problems to solve for time.
4. Quick Tips
- Memorize logs of 2,3,5,10 for easy conversions.
- Use change of base to convert unfamiliar logs to base 10 or e.
5. Mistakes to Avoid
- Misapplying addition/subtraction rules.
- Incorrect change-of-base application.
6. Revision Checklist
- Practice solving for variables inside and outside log expressions.
- Convert exponential to log form quickly.
Summary: Use log laws to simplify calculation and convert exponentials to linear form quickly.
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