Evaluating Logarithms

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Presentation transcript:

Evaluating Logarithms Section 4.4 Notes Evaluating Logarithms

Do-Now: Homework Quiz 1. Phil is trying to build up his endurance so that he can run a marathon. Right now he is able to run 4 miles at a time. Each week he wants to increase his distance by 15%. How far will he be able to run after 13 weeks? Bonus: Is this far enough to finish the marathon? 2. Ralph weighs 350 pounds. He is trying to lose 3% of his body weight every month. Write an equation to represent his weight, y, after x months. How much will he weigh after 16 months?

Units of Measurement For each of the following, give an example of the units of measurement that you might use. 1. speed 2. length 3. weight/force 4. temperature 5. launch angle 6. energy 7. intelligence 8. Dancing ability on DWTS 9. time 10. mass 11. force of electricity

Other measurement scales How do we measure….. 1. Strength of earthquakes Richter scale 2. Intensity of sound volume Decibels 3. Acidity pH scale 4. camera lens speed F-stop

Logarithmic Scales The previous examples all used logarithmic scales. An increase of one unit corresponds to a multiplication of another unit. They are used to simplify calculations for numbers that vary greatly.

Solve the following equations. 1. 5x – 14 = 8 2. 3x3 = 48 3. 4x2 – 12 = 3x2 + 13 4. 5 ∙ 10x = 120

Logarithms What method did you use in #1-3 that you were unable to use in number 4? Logarithms are the inverse operation for an exponential function.

Definition of logarithm logby = x is in logarithmic form bx = y is in exponential form They are equivalent expressions.

Examples Remember that log381 = 4 because 34 = 81. Calculate the following. 1. log464 2. log232 3. log1/525 4. log642 5. log99

Common log and natural log When a log has the base 10, we call it common log or just log. (log10x = log x) What is log 10,000? What is log .001? When a log has the base e, we call it natural log or ln. What is ln 50? (use your calculator) Log and ln are the only logarithms that you can do directly in the calculator.

Logarithms and Exponential Functions as Inverses. Again, logbx and bx are inverse functions. With that in mind, simplify the following. 1. log 105 2. eln 12 3. log8 84 Sometimes you have to rewrite a number so that the log base and the exponent base are the same. 4. log 100x 5. log327x

Finding Inverses Find the inverse of the following functions. 1. y = 8x 2. y = ln (x – 4)