The Laws of Logs

1
The Laws of Logs
2
Multiplication Law

• Investigate
• Any relationships?

3
Proving the Multiplication Law
Log10x b
Log10y c
simplify
xy 10b x 10c
The Multiplication Law
Logax Logay Logaxy
4
The Division Law

• Investigate
• Any relationships?

5
Proving the Division Law
Log10x b
Log10y c
simplify
x y 10b 10c
The Division Law
Logax - Logay Loga(x y)
6
The Power Law

• Investigate
• Any relationships?

7
The Power Law
The Power Law
Loga(x)k kLogax
When k -1
A fact
Loga(1/x) -Logax
8
Write as single logarithms

• log36 log37
• log215 - log23
• 2log53 3log52
• log103 4log10(1/2)

p43 Ex3D