Unit: Logarithms (Logs)

Transcription

1 Unit: Logarithms (Logs) NAME Per /8 pep rally Introduction of Logs HW: Selection from Part 1 /1 ELA A.11A Introduction & Properties of Logs (changing forms) /1 ELA A.11A Properties of Logs (epand & condense rules) /-/ A.11A/A.11BCDEF Practice - Properties of Logs (epand & condense rules) / A.11BCDEF Solving Logs (equations & *inequalities) HW: Selection from Part 1 HW: Selection from Part 1 Properties of Logs (change of ase) HW: Selection from Part HW: Selection from Part 1 /7 A.11BCDEF Solving Logs (equations & *inequalities) /8 A.11BCDEF QUIZ Practice /9-/10 A.11BCDEF Compound & Continuously Compound interest (solve for time: inverse) /11 A.11ABC Graph Logs (PF, a, h, k, domain, range) HW: Part HW: Selection from Pt HW: Part /1 A.11ABCDEF Practice /1 A.11ABCDEF Review /16-/17 (Normal Block Day) TEST: Log Functions /17 HOLIDA Ojectives: Apply properties of logarithmic functions. Solve logarithmic functions for the given variale. Solve applications of logarithmic functions. Graph logarithmic functions from the parent function. Translate etween eponential and log functions. Descrie the relationship etween eponential and logarithmic functions. How are the graphs of the eponential and logarithmic functions related? Identify the general shape of eponential and logarithmic graphs. Know the restrictions on domain and range. Essential Questions: Descrie items that would restrict domain and range in real life. Descrie how to find the solution to a log equation using graphs. Descrie how to find the solution to a log equation using tales. Descrie how to find the solution to a log equation using algeraic methods.

2 Properties of Logs 1. Changing Forms log a a = ase; a = argument. Sum of Logs When you add, you multiply the logs, log m log n log mn. Difference of Logs When you sutract, you divide the logs,. Multiply Numer with Logs. Logs in Calculator (Log) log mlog n log n When you multiply a numer with a log, you raise the argument to that power m plog m log m p When you have no ase, the ase = 10. log m log 10 m *utton on calculator 6. Natural Logs (Ln) When you have Ln, the ase is e. ln m log e m *utton on calculator 7. Change Base When the ase is not 10. Make sure to close the log10 m parenthesis at the top. log m log 8. Solving Logs Get y itself. The inverse of log is eponents. If there is only one log, turn it into an eponent. If is in the eponent, turn it into a log. 9. Canceling Logs If there is only 1 log with the same ase on each side of an equation, then you can cancel the logs. 10 log log log 7 log 8 log log 6 log log log 9 log 0 log10 0 loge 0 ln 0 log10 log log log ( 1) log log log 6 6

3 Notes and Eamples: Logarithms Changing Forms etween Log and Eponential Eamples: Write in log form Common Log log a a Natural Log log ln m m e m e.. e Write in eponential form.. log 6. log 6 7. log ln() 1.86 Evaluate using Mental Math. 9. log 1 1. log 6 1. log 10. log log log 11. log log 17. log Change of Base to evaluate in calculator *the calculator can only do ase 10 logs and ase e logs (Ln) LOG ase 10 LN Natural Log ase e Use a calculator to evaluate each epression. Round to two decimal places. 17. e 19. ln.6 0. ln e When the ase is not 10 you can change the ase to e ale to enter it into the calculator. **Make sure to close the parenthesis at the top. log10 m log m log Use the change of ase formula to evaluate in the calculator. (Hint: put into log form first if needed) 1. log 7 =. = log 11 =. - 8 = (1.) =

4 Condense and Epand (these are VER similar to eponent rules) When you add, you multiply the logs, log m log n log mn When you sutract, you divide the logs, log mlog nlog n When you multiply a numer with a log, you raise the argument to that power m plog m log m p Eamples: Write each as one log. Evaluate if possile. 1. log log. log8 log. log log log log log 1.. ln ( ) ln() 6. ln ln ½ ln y Eamples: Epand into multiple logs 1. log ( ). log. ln ( ) Solving Logs: Get y itself. If there is only 1 log with the same ase on each side of an equation, then you can cancel the logs. If there is only one log, turn it into an eponent. If is in the eponent, turn it into a log. If there are multiple logs on one side, condense them Change forms if needed and solve log log r 7. e 11. log log = 1 1. log 81

5 Change of ase and solve 1. log 7. log. log 9 =. log11 1. log Condense and Solve 1. log 7 = log. 1 log 10 = log 10. * log log( 9) 1. log + log 7 = log 8. log + log =log 6. * log log( 8) Application Prolems Write the equation and solve each prolem. 1. Mr. Perkins invested $8000 in an account paying 7.% interest compounded continuously. A = Pe rt A. Basic Equation: B. How long to the nearest year will it take the money in the account to increase y$000? C. How long to the nearest year will it take the money in the account to doule? D. How long to the nearest year will it take the money in the account to triple? E. -intercept: Domain: Range:

6 18. A population of 0 animals decreases continuously at an annual rate of 16% per year. A = Pe rt A. Basic Equation: B. How long efore there are only 00 animals left? C. How long efore there are only 100 animals left? D. How long efore there are only 0 animals left? E. -intercept: Domain: Range:. The equation h = -0,00 ln p,70 models the relationship etween the elevation, h, aove sea level and the pressure, p, of the surrounding air. A. Basic Equation: B. If a kite s elevation is 00 feet aove sea level, what is the pressure of the surrounding air? C. What if the kite was at 600 feet? D. What if the kite was at 100 feet?

7 Graphing Logs from the Parent Function Logarithm Function: y alog ( h) k Parent Function: Domain: Range: Eamples: 1. y Domain: Range: log 1. y log( 1) Domain: Range:

8 Eplain the transformation etween the logarithmic functions.. From ylog 6( ) to ylog 6( 1).. From yln to y ln Logarithmic Inequalities: dashed or solid shade aove or elow. yln( ) 6. y log( ) 1