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.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations