Name_____________________________________Date_________________Period_________ Algebra II - Worksheet 7.4 A Properties of Logs (09 br) Write each equation in exponential form. 1. log2 64 = 6 2. log4 1 = -3 64 3. log10 (0.01) = -2 Write each equation in logarithmic form. 4. 25 = 32 5. 5-1/2 = 5 5 6. 10-1 = 0.1 Evaluate the expression. Hint—set = x and solve for x. 7. log2 8 8. log8 64 11. log6 1 12. log8 15. log5 5 1 8 9. log6 216 13. log7 1 49 10. log7 7 14. log9 1 27 16. log9 3 17. log2 16 18. log1/2 16 Solve for x. 19. log6 x = 2 20. log5 x = 3 21. log16 x = -1 22. log9 x = 2 23. log1/4 x = -2 24. logx 64 = 3 25. logx 8 = - 1 Expand the expression using the properties of logs. The word log will be used repeatedly in each problem. x 27. log2 28. log10 xy2 26. log6 3x 5 29. log4 xy 3 30. log3 x2yz 31. log5 2x Condense the expression using the properties of logs. The word log will be used once in each problem. 32. log3 7- log3 x 33. 2 log5 x + log5 3 34. log4 5 + log4 x + log4 y 35. 3 log10 x – log10 4 36. 2 log2 x – 3 log2 y 37. log3 4 + 2 log3 x – log3 5 38. log2 x – 2 logs y 39. 3loga 2 + loga 6 – 2 loga 4 Condense the left side of the equation, then solve for x. 40. 2 log4 3 = log4 x 41. log10 x + log 10 3 = log10 12 43. 2 log3 2 = log3 x 44. 3 log10 x = log10 27 42. log3 5 – log3 x = log3 2 45. 3 log5 2 + log5 x = log5 24