Problem 1SP: Use the properties of logarithms to simplify the expressions. log 5 1 + log 5 5 Problem 2SP: Use the properties of logarithms to simplify the expressions. 15 log 15 7 Problem 3SP: Use the properties of logarithms to simplify the expressions. log 1 / 3 ( 1 3 ) c Problem 4SP: Write the expression as the sum or difference of logarithms of a , b , and c . Assume all... Problem 5SP: Write the expression as the sum or difference of logarithms of a and b . Assume a > b . log... Problem 6SP: Write the expression as the sum or difference of logarithms of a , b , and c . Assume all... Problem 7SP: Write the expression as a single logarithm, and simplify the result, if possible.
7.
Problem 8SP: Write the expression as a single logarithm, and simplify, if possible.
8.
Problem 1PE: a. Fill in the blanks to complete the basic properties of logarithms. log b b = ________, log b 1... Problem 2PE: For Exercises 2–5, find the values of the logarithmic and exponential expressions without using a... Problem 3PE: For Exercises 2–5, find the values of the logarithmic and exponential expressions without using a... Problem 4PE: For Exercises 2–5, find the values of the logarithmic and exponential expressions without using a... Problem 5PE Problem 6PE: For Exercises 6–9, approximate the values of the logarithmic and exponential expressions by using a... Problem 7PE: For Exercises 6–9, approximate the values of the logarithmic and exponential expressions by using a... Problem 8PE: For Exercises 6–9, approximate the values of the logarithmic and exponential expressions by using a... Problem 9PE Problem 10PE: For Exercises 10–13, match the function with the appropriate graph. f ( x ) = 4 x Problem 11PE: For Exercises 10–13, match the function with the appropriate graph. q ( x ) = ( 1 5 ) x Problem 12PE: For Exercises 10–13, match the function with the appropriate graph.
12.
Problem 13PE: For Exercises 10–13, match the function with the appropriate graph. k ( x ) = log 1 / 3 x Problem 14PE: 14. Select the values that are equivalent to.
a.
b.
c.
Problem 15PE: Select the values that are equivalent to log 2 2 3 . a. 3 log 2 2 b. log 2 8 c. 3 Problem 16PE: 16. Select the values that are equivalent to.
a. 4
b. 4 log 10
c.
Problem 17PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 3 3 Problem 18PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 10 Problem 19PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 5 5 4 Problem 20PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 4 4 5 Problem 21PE: For Exercises 17–40, evaluate each expression. (See Example 1.) 6 log 6 11 Problem 22PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
22.
Problem 23PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
23.
Problem 24PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
24.
Problem 25PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
25.
Problem 26PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
26.
Problem 27PE: For Exercises 17–40, evaluate each expression. (See Example 1.) 10 log 9 Problem 28PE: For Exercises 17–40, evaluate each expression. (See Example 1.) 8 log 8 5 Problem 29PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 1 / 2 1 Problem 30PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 1 / 3 ( 1 3 ) Problem 31PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 2 1 + log 2 2 3 Problem 32PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 10 4 + log 10 Problem 33PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
33.
Problem 34PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 7 7 + log 4 4 2 Problem 35PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 1 / 4 ( 1 4 ) 2 x Problem 36PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 2 / 3 ( 2 3 ) p Problem 37PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
37.
Problem 38PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log y y 2 Problem 39PE: For Exercises 17–40, evaluate each expression. (See Example 1.)
39.
Problem 40PE: For Exercises 17–40, evaluate each expression. (See Example 1.) log 6 6 4 − log 10 4 Problem 41PE: Compare the expressions by approximating their values on a calculator. Which two expressions are... Problem 42PE: 42. Compare the expressions by approximating their values on a calculator. Which two expressions are... Problem 43PE: Compare the expressions by approximating their values on a calculator. Which two expressions are... Problem 44PE: 44. Compare the expressions by approximating their values on a calculator. Which two expressions are... Problem 45PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 46PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 47PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 48PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 49PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 50PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 51PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 52PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 53PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 54PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 55PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 56PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 57PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 58PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 59PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 60PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 61PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 62PE: For Exercises 45–62, expand into sums and/or differences of logarithms. Assume all variables... Problem 63PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 64PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 65PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 66PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 67PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 68PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 69PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 70PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 71PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 72PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 73PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 74PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 75PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 76PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 77PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 78PE: For Exercises 63–78, write the expressions as a single logarithm and simplify if possible. Assume... Problem 79PE: For Exercises 79–90, find the values of the logarithms given that, and.
79.
Problem 80PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 81PE: For Exercises 79–90, find the values of the logarithms given that, and.
81.
Problem 82PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 83PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 84PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 85PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 86PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 87PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 88PE: For Exercises 79–90, find the values of the logarithms given that, and.
88.
Problem 89PE: For Exercises 79–90, find the values of the logarithms given that, and.
89.
Problem 90PE: For Exercises 79–90, find the values of the logarithms given that log b 2 ≈ 0.693 , log b 3 ≈ 1.0999... Problem 91PE: 91. The intensity of sound waves is measured in decibels and is calculated by the formula
where ... Problem 92PE: The Richter scale is used to measure the intensity of an earthquake and is calculated by the formula... Problem 93PE: 93. a. Graph and state its domain.
b. Graph and state its domain.
c. For what values of x are... Problem 94PE: a. Graph Y 1 = log ( x − 1 ) 2 and state its domain. b. Graph Y 2 = 2 log ( x − 1 ) and state its... format_list_bulleted