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1) Write in exponential form. log 27 9 = x 3) Evaluate. Warm-Up 2) Write in logarithmic form. 5 x = 2003 4) Write the Equation that models this situation:

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Presentation on theme: "1) Write in exponential form. log 27 9 = x 3) Evaluate. Warm-Up 2) Write in logarithmic form. 5 x = 2003 4) Write the Equation that models this situation:"— Presentation transcript:

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2 1) Write in exponential form. log 27 9 = x 3) Evaluate. Warm-Up 2) Write in logarithmic form. 5 x = 2003 4) Write the Equation that models this situation: The current world population of Oompa-loompas is 7,986. If the Ooompa-loompa population grows steadily at a rate of 19% per year, what will their total population be in 10 years?

3 U3 Properties of Logarithms

4 Properties of Logarithms log a 1 = 0 log a a = 1 log a a x = x If log a x= log a ythen x = y because a 0 = 1 because a 1 = a Change-of-Base Product Property Quotient Property Power Property

5 Remember Common Logarithm?? log 10 Is the “common” logarithm This is the LOG button on the calculator Sometimes we’re lazy and we don’t even write the base… log 10 7 = log 7

6 Basic Properties of Logarithms 1) log a 1 = 0 2) log a a = 1 because a 0 = 1 because a 1 = a

7 3) One-to-one Property: If log a x = log a y then x= y

8 Product Property = log a M + log a N1) log a MN = log b A + log b T2) log b AT = log M + log A + log T + log H3) log MATH Express as a sum of logarithms.

9 Express as a single logarithm = log 5 (19*3) Ex. 4) log 5 19 + log 5 3 5) log C + log A + log B + log I + log N = log CABIN

10 Express as a sum of logarithms, then simplify Ex. 6) log 2 (4*16)= log 2 4 + log 2 16 = 2 + 4 = 6

11 Use log 5 3 = 0.683 and log 5 7 = 1.209 to approximate… Ex. 7 log 5 (21) = log 5 3 + log 5 7 = 0.683 + 1.209 = 1.892 = log 5 (3*7)

12 Quotient Property

13 Express as the difference of logs Ex. 1) 2)

14 Use log 5 3 = 0.683 and log 5 7 = 1.209 to approximate… Ex. 3 = log 5 3 - log 5 7 = 0.683 - 1.209 = -0.526

15 Power Property

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17 Express as a product. = -5 * log b 9 Ex. 4) 5)

18 Use log 5 3 = 0.683 and log 5 7 = 1.209 to approximate… Ex. 6 = log 5 7 2 = 2(1.209) = 2.418 log 5 49 = 2 log 5 7

19 Ex. 7 log 10 5x 3 y log 10 5+ log 10 y+ log 10 x 3 log 10 5+ log 10 y+ 3 log 10 x Expand.

20 Expand Simplify the division. Simplify the multiplication of 4  Change the radical sign to an exponent Express the exponent as a product Ex. 8

21 Ex. Condense. 9) 10)

22 Condense Express all products as exponents Simplify the subtraction. Change the fractional exponent to a radical sign. Simplify the addition. Ex 11

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24 Change-of-Base this allows us to change from any base to base 10

25 Ex. 1 Evaluate. Round to four decimal places. Be careful about the parenthesis in the calculator… log(7) / log(3) = 1.7712

26 Ex. 2 Evaluate. Round to four decimal places. = 0.2626


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