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Logarithms log Short form Base a Base a
Base 10 Base 10
Pg 111 Pg 112
Number base 10 Base is 10 Find the answer using calculator = 3 or = 103 3 = 1000 = 1000
Number not base 10 Check answer using calculator Cannot use calculator antilog for number not base 10
Basic Laws of Logarithms Same base number
1 = 2 = 3 =
1. Move number becomes power 3 2. Two log becomes one log using Law of log
1. Move number becomes power 2 3. Three log becomes one log using Law of log 2.
1. Try to use number2, 3 and 5 2. = = =
1. Try to use number2, 3 and 5 2. = = = = 3. +
Basic Laws of Logarithms base number not the Same
use use use Base c can be any number
Example: 2.
Example: 2. Use Law of log 3. 4. 8 or
Natural Logarithms base number e
Pg 118 Base e and base 10 will give same final answer.
Solve equation Find the value of x
Example 1 Take log10 for both sides 2. expand 3. put together 4.
Example 2 Convert to same base 3 2. All terms X 2 3. Index form
Example 3 1. 10 is moved so that “1” 2. ln for both sides
