Intro to Logarithms (start taking notes)

A logarithm is … An Exponent!

Convert from one form to another 103 = 1000 Convert from one form to another 103 = 1000 log101000=3 (log equals exp) Exponential to log form: Log form to exponential form bx=a  logba = x logba = x  bx=a

Convert from one form to another 103 = 1000 Convert from one form to another 103 = 1000 log101000=3 (log equals exp) Exponential to log form: Log form to exponential form bx=a  logba = x 26=64  log264 = 6 41=4  50=1  5-2 = 1/25  3x=81  logba = x  bx=a You fill in

Convert from one form to another 103 = 1000 Convert from one form to another 103 = 1000 log101000=3 (log equals exp) Exponential to log form: Log form to exponential form bx=a  logba = x 26=64  log264 = 6 41=4  log44=1 50=1  log51=0 5-2 = 1/25  log51/25 = -2 3x=81  log381 = x logba = x  bx=a check

Convert from one form to another 103 = 1000 Convert from one form to another 103 = 1000 log101000=3 (log equals exp) Exponential to log form: Log form to exponential form bx=a  logba = x 26=64  log264 = 6 41=4  log44=1 50=1  log51=0 5-2 = 1/25  log51/25 = -2 3x=81  log381 = x logba = x  bx=a log10100=2 102=100 log749 = 2  log81/8 = -1  log55=1  log 121=0  Fill in

Convert from one form to another 103 = 1000 Convert from one form to another 103 = 1000 log101000=3 (log equals exp) Exponential to log form: Log form to exponential form bx=a  logba = x 26=64  log264 = 6 41=4  log44=1 50=1  log51=0 5-2 = 1/25  log51/25 = -2 3x=81  log381 = x logba = x  bx=a log10100=2 102=100 log749 = 2 72=49 log81/8 = -1 8-1=1/8 log55=1 51=5 log 121=0 120=1 Check

On Intro to Logs worksheet… Scoot desks to work with your partner You are ready to do #1-25, 30-31 If it says evaluate, your answer is one number Remember – a log is an exponent For #17-25, the answer to a log is the missing exponent No base? It’s assumed to be base 10 This should take 7-10 min

Properties of Logarithms (more notes) 1. Product Property logbmn = logbm + logbn (to accomplish multiplication, add exponents. Logs are exponents) Ex Simplify: log42+log432 log4 2•32 log464 3 Simplify means: Combine into one log Evaluate if possible

Properties of Logarithms (more notes) 2. Quotient Property logb = logbm - logbn (to accomplish division, subtract exponents. Logs are exponents) Ex Simplify: log232-log24 log2 32/4 log28 3 Simplify means: Combine into one log Evaluate if possible

Properties of Logarithms (more notes) 3. Power Property logbap = p•logba (the log is an exponent. For power to a power, multiply exponents) Ex Simplify: log3812 2•log3 81 2•4 8 Simplify means: Express as a product Evaluate if possible

Properties of Logarithms (more notes) 4. Inverse Properties (logs are inverse properties of exponents) logbbx = x log10107 = 7

You are ready to finish your worksheet… #26, 28 use quotient property #27 use product and power properties. Put the 2 back on the 5 as an exponent #29, 32 use inverse properties #35: 9x=1/27 Rewrite as powers of 3. Solve like prev WS Back side of WS: #1,5 use power property Expand means separate into multiple logs, no exponents Simplify means combine into just one log. Evaluate if possible.