New Topic Exponents Exponential Equations I Exponential Functions The Exponential Function Base e The Logarithm Functions Logarithmic & Exponential Equations Applications:Growth & Decay Review&Test

UNIT 5  : EXPONENTIAL & LOGARITHMIC FUNCTIONS

LESSON 6: LOGARITHMIC EQUATIONS

The following properties of logarithms are important and used frequently in our study of logarithms.

They correspond closely to our rules for exponents studied earlier.

Note:  When we read  log28, we ask the question  To what exponent must base 2 be raised to give 8?  The answer is of course 3

and this idea gives rise to the following definition.

Definition:  the expression  logax  is defined to mean   the exponent to which base a must be raised to give x.

The expression reads:   the logarithm of x, base a

Hence  log10100 means the exponent to which base 10 must be raised to give 100.  The answer is 2, giving the statement  log10100 = 2.

Hence  log381 means the exponent to which base 3 must be raised to give 81.  The answer is 4, giving the statement  log381 = 4.

Note:  See # 12 in homework questions for more examples