Unit on Logarithms by Curtis Hoier

1. BY YOUR POWERS COMBINED
UNIT IN LOGARITHMS

2. BACKGROUND
3 + 3 + 3 + 3 = 4 × 3 = 12
4
Multiplicati
on:
Division:
12 ÷ 4 = 3 OR 12 ÷ 3 = 4
“What number you add
to itself 4 times to get
12?
“How many times you
add 3 to itself to get
12?
Multiplication and Division are inverse
operations.
Division is the operation you use to find
the starting place of a multiplication
problem.

3. SAMPLE PROBLEMS FROM TEXTBOOK

4. LOGARITHM BASICS
log3 81= 4
The exponent to put on a base of 3 to get 81
is 4
Just like Division is the inverse of
multiplication…
Logarithms are the inverse of
exponents.
3 × 3 × 3 × 3 = 34
= 81
4
Multiplicati
on:

5. COMMON USES FOR LOGARITHMS
• Chemistry (pH scale)

6. COMMON USES FOR LOGARITHMS
• Noise Level (decibels)

7. COMMON USES FOR LOGARITHMS
• Earthquake Magnitudes (Richter
scale)

8. VIHART ON LOGARITHMS

9. SAMPLE PROBLEMS FROM TEXTBOOK
Problems taken from:
https://maths.mq.edu.a
u/numeracy/web_mums
/module2/Worksheet27/
module2.pdf

10. RULES - SUM OF LOGARITHMS
Logarithms:
log3 81 + log3 9 = log3(81 × 9)
The sum of the exponents you put on 3 to get
81 and 9 respectively is equal to the
exponents you put on 3 to get (81 × 9)
Logarithm rules are the same as the
rules for exponents – just with fancy
wording.
34 × 32 = 34+2 = 36
Exponents:
81 × 9 = 729

11. RULES - DIFFERENCE OF LOGARITHMS
Logarithms:
log3 81 − log3 9 = log3(81 ÷ 9)
The difference of the exponents you put on 3
to get 81 and 9 respectively is equal to the
exponents you put on 3 to get (81 ÷ 9)
Logarithm rules are the same as the
rules for exponents – just with fancy
wording.
34 ÷ 32 = 34−2 = 32
Exponents:
81 ÷ 9 = 9

12. RULES – PRODUCT OF LOGARITHMS
Logarithms:
(log3812
) = 2 × log381
The exponent you put on a base of 3 to
get 812
is equal to 2 times the exponent you
put on 3 to get 81
Logarithm rules are the same as the
rules for exponents – just with fancy
wording.
(34)2 = 34×2 = 38
Exponents:
812
= 6561

13. SAMPLE PROBLEMS FROM TEXTBOOK
Problems taken from:
https://maths.mq.edu.a
u/numeracy/web_mums
/module2/Worksheet27/
module2.pdf

14. SOME FUN TO WRAP UP