Math Review Low Of Logarithms, Set, Directed Graphs and Functions, Summations, Mathematical Induction, Basic Number Theory

Laws Of Logarithms

• $y = log_b(x)$ meaning $b^y$

• $log_2(x) = log_2(x)$

• $log^n(x) = (log(x))^n$

• $ln(x) = log_e(x)$ (e ≈ 2.71828)

• $log_b(xy) = log_b(x) + log_b(y)$

• $log_b(x/y) = log_b(x) - log_b(y)$

• $log_b(x) = \frac{log_a(x)}{log_a(b)}$

• $0 < x < y \Rightarrow \log_b(x) < \log_b(y)$

• $log_b1 = 0$

• $log_bb = 1$

• $log_b(x) < x \quad \text{(for } b \geq 2 \text{ and } x > 0)$

• $log 1024 = 10$

• $ln 2 \approx 0.693 \quad \text{(in particular, } 0 < \ln 2 < 1 \text{)}$

• $log e \approx 1.44 \quad \text{(in particular, } 1 < \log e < 2 \text{)}$