Transcript The Laws of Logs

The Laws of Logs
Multiplication Law
• Investigate
• Any relationships?
Proving the Multiplication Law
Rewriting as powers
Log10x = b
Log10y = c
xy =
10b
x
10c
simplify
write as logs
The Multiplication Law
Logax + Logay = Logaxy
The Division Law
• Investigate
• Any relationships?
Proving the Division Law
Rewriting as powers
Log10x = b
10b = x
Log10y = c
10c = y
x÷y=
10b ÷
10c
simplify
write as logs
The Division Law
Logax - Logay = Loga(x ÷ y)
The Power Law
• Investigate
• Any relationships?
The Power Law
The Power Law
Loga(x)k =kLogax
When k = -1
A fact
Loga(1/x) =-Logax
Write as single logarithms
1. log36 + log37
2. log215 - log23
3. 2log53 + 3log52
4. log103 – 4log10(1/2)
p43 Ex3D