BELL RINGER Write, in paragraph form, everything you remember about logarithmic and exponential functions including how to convert, solve logarithmic equations, and how to change base.

LOGARITHMS Wednesday, October 28, 2015

 Exponential GRAPHS  Logarithmic

INVERSE

NOTES  The inverse of an exponential function is a common logarithmic function.  Convert from exp. to log  b x = y  log b y = x  Convert from log to exp.  log b y = x  b x = y  Calculators only do log 10 aka “common log”, so log is really log base 10.  Change of Base  log b a = log a log b  The inverse of natural log [ln(x)] is base e (Euler’s number).  Convert from natural log to base e  ln y = x  e x = y  Convert from base e to natural log  e x = y  ln y = x

PROPERTIES OF LOGS-- NOTES There are 7 laws of exponents and 3 properties of logarithms that you need to know. Remember, logarithms are the inverse of exponentials and some rules apply…

PROPERTIES OF LOGS-- NOTES 1)log b m + log b n= log b mn 2) log b m – log b n = log b m n 3) p log b m = log b m p

SOLVING LOG EQUATIONS 1.If possible, get log of the same bases equal and “drop the log.” 2.If not, then change to exponential form and solve.

TWO PROPERTIES

EXAMPLES

THREE STRATEGIES

PRACTICE  LOG PROPERTIES CLASSWORK  LOG PROPERTIES HOMEWORK