Logarithms
Logarithms
Logarithms express exponents: log_b(x) = y means b^y = x. They convert multiplication to addition and division to subtraction, making large-number calculations manageable in competitive exams.
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
When multiplying two numbers under a single log
Quotient Rule
log(m / n) = log m − log n
When dividing numbers under a log
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.