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Law of Logarithms

Law of Logarithms. How do we write an exponential equation as a logarithmic equation?. Rewrite 3 ² = 9 as a logarithmic equation. log 3 9 = 2 Write the following exponential equations as logarithmic equations. 8 2 = 64 2) 10 0 = 1 3) 3 -2 = 1/9. Law of logs.

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Law of Logarithms

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  1. Law of Logarithms

  2. How do we write an exponential equation as a logarithmic equation? • Rewrite 3² = 9 as a logarithmic equation. • log3 9 = 2 • Write the following exponential equations as logarithmic equations. • 82 = 64 2) 100 = 1 3) 3-2 = 1/9

  3. Law of logs • They are similar to exponent rules… 1) Bx = Y  logB Y = X 2) logB X = logB Y  X = Y 3) logB X + logB Y = logB (XY) and logB X - logB Y = logB (X/Y) 4) Z● logB X = logB Xz

  4. Write the following logarithms as 1 logarithm • log5 10 + log5 6 2) log4 6 + log4 3 3) 3 log6 2 4) 2 log3 3 + log3 4 5) (1/2)log2 25 + log2 2 - log2 5 6) 4 log3 3 + log3 x - log3 5

  5. Evaluating Logs • Evaluate log74 • just use your calculator… • The log with the base is ALWAYS THE DENOMINATOR!!! • (log(4))/(log(7))

  6. Solving Logarithmic Equations • log7n = (2/3)log78 • log6x + log69 = log654 • log9(3x+14) – log95 = log9(2x) • log10(3x – 5) + log10 x = log102 • log10 4 + log10x = 2

  7. Solve each equation.

  8. Solve continued…

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