1. Intro to Logarithms
(start taking notes)

2. A logarithm is …
An Exponent!

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

4. Convert from one form to another 103 = 1000
Convert from one form to another 103 = 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

5. Convert from one form to another 103 = 1000
Convert from one form to another 103 = 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

6. Convert from one form to another 103 = 1000
Convert from one form to another 103 = 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

7. Convert from one form to another 103 = 1000
Convert from one form to another 103 = 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

8. 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

9. 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

10. 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

11. 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

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

13. 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.