Log Rules

Logarithm problems test your knowledge of fundamental log properties:

• Definition: $\log_a b = x \iff a^x = b$
• Power Rule: $\log_a (b^n) = n \log_a b$
• Addition/Subtraction: $\log_a b + \log_a c = \log_a(bc)$ and $\log_a b - \log_a c = \log_a(b/c)$
• Change of Base: $\log_a b = \frac{\log_c b}{\log_c a}$

Approximations are also common: $\log_{10} 2 \approx 0.3$, $\log_{10} 5 \approx 0.7$, $\ln 2 \approx 0.7$, $\ln 10 \approx 2.3$.