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The Laws of Logs

The Laws of Logs. Multiplication Law. Investigate Any relationships?. Rewriting as powers. write as logs. Proving the Multiplication Law. Log 10 x = b. Log 10 y = c. simplify. xy = 10 b x 10 c. The Multiplication Law. Log a x + Log a y = Log a xy. The Division Law. Investigate

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The Laws of Logs

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  1. The Laws of Logs

  2. Multiplication Law • Investigate • Any relationships?

  3. Rewriting as powers write as logs 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. Rewriting as powers 10b = x 10c = y write as logs 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

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