Exam 4: Exponential and Logarithmic Functions

Graph the function - $\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { x - 3 } + 4$

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\ln ( x - 3 ) - \ln ( x + 5 ) = \ln ( x - 3 ) - \ln ( x + 7 )$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 10 ^ { 2 } } + \log _ { 10 ^ { 5 } }$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Graph the function -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 ^ { x + 3 } + 2$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 4 } ( x - 7 ) - \log _ { 4 } ( x + 1 )$

Write the equation in its equivalent logarithmic form. - $\sqrt [ 3 ] { 8 } = 2$

Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $1020 at 6% compounded annually for 19 years.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \mathrm { M } ^ { - 10 }$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { W } \left( \frac { 9 x } { 4 } \right)$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $2 \log _ { 3 } 5 + \frac { 1 } { 3 } \log _ { 3 } ( r - 2 ) - \frac { 1 } { 2 } \log _ { 3 } r$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $6 \ln x - \frac { 1 } { 4 } \ln y$

Evaluate or simplify the expression without using a calculator. - $8 \left( 10 ^ { \log 2.1 } \right)$

Solve the problem. -The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 16,000 } { 1 + 399.0 \mathrm { e } ^ { - 1.2 t } }$ models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people became ill with this infection when the epidemic began?

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log x + \log 2$

Graph the function - $\text { Use the graph of } f ( x ) = e ^ { x } \text { to obtain the graph of } g ( x ) = e ^ { - x }$

Graph the function -Use the graph of $f ( x ) = 4 ^ { x }$ to obtain the graph of $g ( x ) = 4 ^ { - x }$ .

Evaluate or simplify the expression without using a calculator. - $\log 1000$

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 3 } ( x + 2 ) - \log _ { 3 } x = 2$