Logarithms- Expand, Condense, Evaluate

The letter 'k' indicates the vertical shift of the function, telling us if the function has moved up or down.

The letter 'a' indicates the vertical stretch, compression, or reflection of the function.

The change of base formula is log_b(a) = log_c(a) / log_c(b), where c is any positive number.

The function y = log(x+3) represents a leftward shift of 3 units.

Use the change of base formula: log_b(x) = log(x) / log(b) using common or natural logarithms.

The domain is x > 0, meaning the input must be positive.

The range is all real numbers, (-∞, ∞).

Condensing logarithmic expressions means to combine multiple logs into a single log using properties of logarithms.

The product property states that log_b(m*n) = log_b(m) + log_b(n).

The quotient property states that log_b(m/n) = log_b(m) - log_b(n).