Logarithms
Logarithms
Logarithms reverse exponentiation: log_b(x) = y means b^y = x. Exams test simplification using product, quotient, and power rules, along with base-conversion and standard log values. SSC CGL Tier 1 and Tier 2 each carry 1\u20132 log questions. Memorize log 2, log 3, and log 7 to solve numerical evaluations within seconds.
Key Idea
If log_b(x) = y, then b^y = x. Logarithm is the inverse of exponentiation — log_10(1000) = 3 because 10^3 = 1000.
Core Formulas
Product Rule
log(m × n) = log m + log n
Split a product inside a log into a sum \u2014 use this to break down log(12) into log 4 + log 3 or similar.
Quotient Rule
log(m / n) = log m − log n
Convert a division inside a log into a subtraction \u2014 apply when simplifying expressions like log(50/2).
Power Rule
log(m^n) = n × log m
When the argument has an exponent — bring the power in front
Change of Base
log_b(x) = log x / log b (common logs)
To convert between bases — especially log base 2 or base 5 problems
Standard Values
log 2 ≈ 0.301 | log 3 ≈ 0.477 | log 7 ≈ 0.845 | log 10 = 1
To evaluate numerical log expressions without a calculator
Relevant Exams
Logarithms appear in SSC CGL Tier 1 and Tier 2, usually 1–2 questions. Common question types: find log value given standard values, simplify log expressions, find x in log equations, and base-conversion problems.