Name_____________________________________Date_________________Period_________ Properties of Logs Name___________________________________Date_____________Period_______ Expand the expression using the...

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Name_____________________________________Date_________________Period_________ Properties of Logs Name___________________________________Date_____________Period_______ Expand the expression using the properties of logs. The word log will be used repeatedly in each problem. 1. log6 3x 2. log2 x 5 3. log10 xy2 4. log4 xy 3 5. log5 2 x 6. log m a yw 7. ln x1/2yz 8. ln 5x3 9. x ln y æö ç÷ èø 10. log6 5x³y²z 11. log2 3( x 5 ) 12. log10 3x⁵y2 Condense the expression using the properties of logs. The word log will be used once in each problem. 1. log3 8 - log3 2 2. 2 log5 4 + log5 3 3. log4 5 + log4 3 + log4 1 4. 1 2 log10 24 – log10 4 5. 2 3 log2 x – 3 log2 y 6. log3 4 + 2 log3 x – log3 5 7. 1 2 log2 x – 2 logs y 8. 3loga 2 + 1 3 loga 27 - 1 2 loga 16 9. ln x + ln 5 10. log3 8x - log3 27y 11. 2 log5 4x + log5 5x 12. log4 5x + log4 3y + log4 z 13. ln 4 – ln y 14. 4 ln x + 5 ln y 15. ln 6 – (ln x + ln 3) 16. ln 4 + 3 ln x + ½ ln y 17. ln 4x – ln 3y 18. 2 ln x + 3 ln y 19. ln 6y – (ln x + ln 2) 20. ln 7 + 2 ln x + ½ ln 3y _1103806459.unknown _1295353815.unknown LESSON Name_________________________________ Date______________________ Period________ Practice A Inverses of Relations and Functions Graph the relation and connect the points. Then graph the inverse. Identify the domain and range of each relation. 1 () 2 fxx =+ 1. a. Plot the ordered pairs and draw a curve through the points. b. Identify the domain and range for the relation. c. Switch the x- and y-values for each ordered pair and plot those points. Draw a curve through the points. d. Identify the domain and range for the inverse. Use inverse operations to write the inverse of each function. 2. f (x)  2x  9 a. Undo the subtraction by b. Undo the multiplication by c. f1(x)  __________________________ 3. f (x)  4x 4. f (x)  x  6 5. f (x)  3x  12 6. f (x)  6  10x 7. f (x)  7x  1 8. f (x)  22x Solve. 9. Holly paid $9.89 for lunch, including a 15% tip. What was the cost of her food? a. Write an equation for the total cost, c, as a function of the cost of the food, x. b. Find the inverse function that models the cost of the food as a function of the total cost. c. Evaluate the inverse function for c  9.89. Practice B Inverses of Relations and Functions Use inverse operations to write the inverse of each function. 1. f (x)  15x  10 2. f (x)  10  4x 3. f (x)  12  9x 4. f (x )  5x  2 5. f (x )  x  6 6. 7. () 12 x fx =- 8. 12 () 4 x fx - = 9. 31 () 6 x fx + = Graph each function. Then write and graph its inverse. 10. f (x )  2x  4 11. 5 ()2 2 fxx =- Solve. 12. Dan works at a hardware store. The employee discount is determined by the formula d  0.15 (c  10 ). Use the inverse of this function to find the cost of the item for which Dan received an $18.00 discount. a. Find the inverse function that models cost as a function of the discount. b. Evaluate the inverse function for d  18. c. What was Dan’s final cost for this item? x� 0� 1� 2� 4� 6� � y� 3� 4� 5� 6� 7� � Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Algebra 2 _1310403397.unknown _1310403398.unknown _1310403461.unknown _1310403396.unknown _1310403395.unknown Section 2.6 Homework Name_____________________________________Date_______________________Period___________ Section 2.7 Homework Name_____________________________________Date__________________________Period________ Section 4.1 Homework