Question

For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. 15. log(x^15 y^13 / z^19) 16. ln(a^-2 / b^-4 c^5) 17. log(sqrt(x^3 y^-4)) 18. ln(y * sqrt(y / (1 - y))) 19. log(x^2 y^3 * sqrt(x^2 y^5)) For the following exercises, condense each expression to a single logarithm using the properties of logarithms. 20. log(2x^4) + log(3x^5) 21. ln(6x^9) - ln(3x^2) 22. 2log(x) + 3log(x + 1) 23. log(x) - 1/2 log(y) + 3log(z) 24. 4log_7(c) + log_7(a)/3 + log_7(b)/3 For the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base. 25. log_7(15) to base e 26. log_14(55.875) to base 10 For the following exercises, suppose log_5(6) = a and log_5(11) = b. Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of a and b. Show the steps for solving. 27. log_11(5) 28. log_6(55) 29. log_11(6/11) NUMERIC For the following exercises, use properties of logarithms to evaluate without using a calculator. 30. log_3(1/9) - 3log_3(3) 31. 6log_8(2) + log_8(64) / 3log_8(4) 32. 2log_9(3) - 4log_9(3) + log_9(1/729) For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places. 33. log_3(22) 34. log_8(65) 35. log_6(5.38) 36. log_4(15/2) 37. log_1/2(4.7)

          For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.
15. log(x^15 y^13 / z^19) 16. ln(a^-2 / b^-4 c^5) 17. log(sqrt(x^3 y^-4)) 18. ln(y * sqrt(y / (1 - y))) 19. log(x^2 y^3 * sqrt(x^2 y^5))
For the following exercises, condense each expression to a single logarithm using the properties of logarithms.
20. log(2x^4) + log(3x^5) 21. ln(6x^9) - ln(3x^2) 22. 2log(x) + 3log(x + 1)
23. log(x) - 1/2 log(y) + 3log(z) 24. 4log_7(c) + log_7(a)/3 + log_7(b)/3
For the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base.
25. log_7(15) to base e 26. log_14(55.875) to base 10
For the following exercises, suppose log_5(6) = a and log_5(11) = b. Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of a and b. Show the steps for solving.
27. log_11(5) 28. log_6(55) 29. log_11(6/11)
NUMERIC
For the following exercises, use properties of logarithms to evaluate without using a calculator.
30. log_3(1/9) - 3log_3(3) 31. 6log_8(2) + log_8(64) / 3log_8(4) 32. 2log_9(3) - 4log_9(3) + log_9(1/729)
For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.
33. log_3(22) 34. log_8(65) 35. log_6(5.38) 36. log_4(15/2) 37. log_1/2(4.7)

For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.
15. log(x^15 y^13 / z^19) 16. ln(a^-2 / b^-4 c^5) 17. log(sqrt(x^3 y^-4)) 18. ln(y * sqrt(y / (1 - y))) 19. log(x^2 y^3 * sqrt(x^2 y^5))
For the following exercises, condense each expression to a single logarithm using the properties of logarithms.
20. log(2x^4) + log(3x^5) 21. ln(6x^9) - ln(3x^2) 22. 2log(x) + 3log(x + 1)
23. log(x) - 1/2 log(y) + 3log(z) 24. 4log7(c) + log7(a)/3 + log7(b)/3
For the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base.
25. log7(15) to base e 26. log14(55.875) to base 10
For the following exercises, suppose log5(6) = a and log5(11) = b. Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of a and b. Show the steps for solving.
27. log11(5) 28. log6(55) 29. log11(6/11)
NUMERIC
For the following exercises, use properties of logarithms to evaluate without using a calculator.
30. log3(1/9) - 3log3(3) 31. 6log8(2) + log8(64) / 3log8(4) 32. 2log9(3) - 4log9(3) + log9(1/729)
For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.
33. log3(22) 34. log8(65) 35. log6(5.38) 36. log4(15/2) 37. log1/2(4.7)

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