Log Functions Unit 3

What’s a Log? The logarithmic function is the inverse of an exponential function. Therefore, a log is an exponent. (just like diving is multiplying by a fraction)

Log form Exponential Form

The Base of a Log (the calculator only does log and ln…) b, the base of a log, can be any number… For example, log3 9 = ? log6 216 = ? (the calculator only does log and ln…)

The Base of a Log These bases are frequently used: Common log – if the base is not written, it is base 10 Natural log (ln) has a base of e Remember e is an irrational number with a value of approx. 2.718281828

Characteristics of Log Functions Generally, for b > 0, b ≠ 1, x > 0… logb 1 = 0 (because…) logb b = 1 logb bx = x b logb x = x

Characteristics of Common Log Functions For base 10 common logs, x > 0 log 1 = 0 (because…) log 10 = 1 log 10x = x 10 log x = x

Characteristics of Natural Log Functions For base e natural logs, x > 0 ln 1 = 0 (because…) ln e = 1 ln e x = x e ln x = x

Properties of logarithms Product: logb RS = logb R + logb S Quotient: logb R = logb R – logb S S Power: logb Rc = c logb R

Change of Base Formula Here’s how we can use the calculator to evaluate log34 !! logb x = log x log b So, log34 = ?