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Aim: What are the properties of logarithms?

Aim: What are the properties of logarithms?. Do Now: Rewrite the following exponential form into log form. b x = A b y = B. Replace x and y by log b A and log b B. HW:p.331 # 16,18,20,22,24,26,28,38,40,42,48,52. RULES of LOGARITHMS.

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Aim: What are the properties of logarithms?

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  1. Aim: What are the properties of logarithms? Do Now: Rewrite the followingexponential form into log form • bx = A • by = B Replace x and y by logbA and logbB HW:p.331 # 16,18,20,22,24,26,28,38,40,42,48,52

  2. RULES of LOGARITHMS Product Rule:logbAB = logb A + logb B Quotient Rule:logbA/B = logb A - logb B Power Rule:logbAc= c logbA

  3. Example 1. Find the value of log6 12 + log6 3 log6 (12·3) use the product rule = log6 36 simplify Write it as exponential equation 6a= 36 Evaluate a = 2

  4. 2. If 2 log3 9 + log3x = log3 27, find x Simplify left-hand side . Use the power rule, then use the product rule log3 92 + log3x = log3 27 log3 (92· x) = log3 27 log3 (81x) = log3 27 Equate the powers, and solve for x 81x = 27

  5. 3. Ifexpress log10 x in terms of log10a and log10 b Express as a power Write the log to the base 10 of each side the equation Use the quotient rule Use the power rule

  6. 4. The expression log3a5b is equivalent to • 5 log3ab b) 5 log3a + log3b • c) log3 5ab d) log3 5a + log3b Use the product rule log3a5b = log3a5 + log3b Use the power rule = 5 log3 a + log3b

  7. 1. Write the expression in terms of log10 a and log 10b • log10ab • log10 (a2b) a. log10a + log10b b. 2 log10 a + log10b 2. Solve for n: 3 log2 4 = log2n 64 3. Solve for n: log10 1000 – 2 log10 100 = log10n 1/10 or 0.1

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