Lesson 10.2Logarithmic Functions Logarithm: Inverse of exponential functions. “log base 2 of 6” Ex: Domain: x>0 Range: all real numbers Inverse of exponential functions

Loop Conversions Convert each log expression into an exponential expression Convert each exponential expression into a log expression

Example 1Translating a)__________________ b)__________________ c) ______________ d) ______________ ExponentialLogarithmic

Useful Log Properties Exponential Reasoning [1] [2] [3] base - base [4] Cannot take logs of negative number [5] change of base formula (for calculator)

Evaluating Log Expressions To evaluate, answer the question: “the base raised to what power gives you the answer?” Ex:  2 raised to what power equals 8?

Example 2Evaluate using properties (algebraic proof) a) b) c)d) e)

Example 4Clearing Bases Using Logs a) b)

Example 5Clearing Logs Using Exponents a) b) c) d)

Logs on both sides