6. Exponential & Logarithmic Functions

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 98 - ln 13

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 84 - ln 17

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.(1/2)(log x + log y)

Graph each function. Give the domain and range. ƒ(x) = | log￬1/2 (x-2) |

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.(1/2)(log5 x + log5 y) - 2 log5 (x + 1)

The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.

h(x) = ln (2x)

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.(1/3) [2 ln(x + 5) - ln x - ln (x^2 - 4)]

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.log x + log(x^2 - 1) - log 7 - log(x + 1)

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log5 13

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log14 87.5

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log0.1 17

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.logπ 63

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_2 5

In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function.y = log3 x

In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function.y = log2 (x + 2)