Core5 mapped NDA questions
Build the idea
Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.
Concept
A logarithm answers 'to what power must the base be raised to get this number?': if a^x = N then log_a N = x. Logarithms convert multiplication/division into addition/subtraction, which simplifies many calculations.
The common base is 10; the natural base is e.
Key Points & Formulas
- log_a(mn) = log_a m + log_a n.
- log_a(m/n) = log_a m − log_a n.
- log_a(mᵏ) = k log_a m.
- Change of base: log_a m = log_b m / log_b a; and log_a a = 1, log_a 1 = 0.
Worked Example
Q. If log₁₀ 2 = 0.301, find log₁₀ 8.
log₁₀ 8 = log₁₀ 2³ = 3 log₁₀ 2.
= 3 × 0.301 = 0.903.