1. The Laws of Logs

2. Multiplication Law
Investigate
Any relationships?

3. Proving the Multiplication Law
Rewriting as powers
Log10x = b
Log10y = c
simplify
xy = 10b x 10c
write as logs
The Multiplication Law
Logax + Logay = Logaxy

4. The Division Law
Investigate
Any relationships?

5. Proving the Division Law
Rewriting as powers
10b = x
10c = y
Log10x = b
Log10y = c
simplify
x ÷ y = 10b ÷ 10c
write as logs
The Division Law
Logax - Logay = Loga(x ÷ y)

6. The Power Law
Investigate
Any relationships?

7. The Power Law Loga(x)k =kLogax Loga(1/x) =-Logax The Power Law
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