Logarithms Flashcards

Grade 10 · Math · Flashcards

Key definitions, properties, and formulas for logarithms.

Flashcards

Logarithm definition: log_b(x) = y ↔ bʸ = x; the log is the exponent
Common log: log(x) = log₁₀(x); base 10
Natural log: ln(x) = log_e(x); base e ≈ 2.718
log_b(1): Always 0, because b⁰ = 1
log_b(b): Always 1, because b¹ = b
Product rule: log_b(xy) = log_b(x) + log_b(y)
Quotient rule: log_b(x/y) = log_b(x) - log_b(y)
Power rule: log_b(xⁿ) = n · log_b(x)
Change of base formula: log_b(x) = log(x)/log(b) = ln(x)/ln(b)
Inverse relationship: log_b(bˣ) = x and b^(log_b(x)) = x; logs and exponentials undo each other
Domain of log_b(x): x > 0 only; logs of zero or negatives are undefined
Graph of y = log_b(x) (b>1): Passes through (1,0) and (b,1); vertical asymptote at x=0; always increasing
Solving log_b(x) = c: Convert to exponential: x = bᶜ
Richter scale connection: Each whole number increase = 10× greater amplitude; base-10 log of amplitude