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Logarithms

Logarithms. Objective: Students will use properties of logarithms to simplify expressions. Logarithmic Functions. Logarithmic Equation. y = log a x. exponent. /logarithm. x = 2 y is an exponential equation . If we solve for y it is called a logarithmic equation .

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Logarithms

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  1. Logarithms Objective: Students will use properties of logarithms to simplify expressions.

  2. Logarithmic Functions Logarithmic Equation y = loga x exponent /logarithm x = 2yis anexponentialequation. If we solve for y it is called alogarithmic equation. Let’s look at the parts of each type of equation: Exponential Equationx = ay base number In General, a logarithm is the exponent to which the base must be Raised to get the number that you are taking the logarithm of.

  3. base number exponent Example1 : Rewrite in exponential form a) solve loga64 = 2 a2 = 64 a = 8 b) Solve log5 x = 3 Rewrite in exponential form: 53 = x x = 125

  4. c) Solve An equation in the form y = logb x where b > 0 and b ≠ 1 is called a logarithmic function. 7y = 1 = 7-2 49 y = –2 Logarithmic and exponential functions are inverses of each other logb bx = x blogb x = x

  5. Examples 2 Evaluate each:a. log8 84b. 6[log6 (3y – 1)] logb bx = x log8 84= 4 blogb x = x 6[log6 (3y – 1)]=3y – 1 Here are some special logarithm values: 1. loga 1 = 0 because a0 = 1 2. loga a = 1 because a1 = a 3. loga ax = x because ax = ax

  6. Logarithms Consider 72 = 49. The logarithm of 49 to the base 7 is equal to 2 (log749 = 2). Logarithmic form Exponential notation log749 = 2 72 = 49 In general: Ifbx = N, then logbN = x. Ex 3 State in logarithmic form or State in exponential form: a) 63 = 216 log6216 = 3 c) log5125 = 3 53 = 125 d) log2128= 7 27 = 128 log416 = 2 b) 42 = 16

  7. Practice Evaluating Logarithms 1. log2128 2. log327 Note: log2128 = log227 = 7 log327 = log333 = 3 log327 = x 3x = 27 3x = 33 x = 3 log2128 = x 2x = 128 2x = 27 x = 7 3. log556 logaam = m = 6 4. log816 5. log81 log816 = x 8x = 16 23x = 24 3x = 4 log81 = x 8x = 1 8x = 80 x = 0 loga1 = 0

  8. Evaluating Logarithms 6. 7. log4(log338) = x log48 = x 4x = 8 22x = 23 2x = 3 2x = 1 8. = 23 = 8

  9. Evaluating Base 10 Logs Base 10 logarithms are called common logs. EX 4 Using your calculator, evaluate to 3 decimal places: a) log1025 b) log100.32 c) log102 1.398 -0.495 0.301 Common logs may also be written without the base 10 log 25 log 0.32 1og 2 d) ln 15 e) ln 0.12 f) ln 2 .693 -2.120 2.708

  10. Classwork P. 499 guided practice #1-13 Homework page 504 #9-27 odd

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