6. Exponential & Logarithmic Functions

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln (27 * 943)

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. 1/2 ln x - ln y

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.3 ln x - (1/3) ln y

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

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.4 ln (x + 6) - 3 ln x

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 27 + ln 943

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

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.3 ln x + 5 ln y - 6 ln z

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)]