Exam 4: Exponential and Logarithmic Functions

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. - $\log _ { 3 } 6 - \log _ { 3 } 2$

Graph the function by making a table of coordinates. - $f(x)=\left(\frac{1}{4}\right)^{x}$

Graph the function. -Use the graph of $\log _ { 3 } x$ to obtain the graph of $f ( x ) = - \frac { 1 } { 2 } \log _ { 3 } x$ .

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. - $\log ( x + 5 ) = \log ( 4 x - 4 )$

Choose the one alternative that best completes the statement or answers the question. Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $y = 4 ( 3 ) ^ { x }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \sqrt [ 4 ] { \mathrm { y } }$

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. - $3 \ln ( 4 x ) = 6$

Evaluate or simplify the expression without using a calculator. - $\log \left( \frac { 1 } { 100 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } ( 27 x )$

Solve the problem. -The logistic growth function $f ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.29 t } }$ describes the population of a species of butterflies $t$ months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain?

Evaluate or simplify the expression without using a calculator. -In $\mathrm { e }$

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. - $\log _ { 3 } ( x + 6 ) + \log _ { 3 } ( x - 6 ) - \log _ { 3 } x = 2$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $\mathrm { e } ^ { \mathrm { x } } = 5.6$

Evaluate the expression without using a calculator. - $\log _ { 5 } 625$

Write the word or phrase that best completes each statement or answers the question. Present data in the form of tables. For the data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. -Percentage of Population Living in the South Suburbs of a Large City \begin{tabular} { c | c } Year & Percent \\ \hline 1950 & 55 \\ 1960 & 70 \\ 1970 & 74 \\ 1980 & 75 \\ 2000 & 76 \end{tabular}

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { x - 6 } { x ^ { 5 } } \right)$

Graph the function by making a table of coordinates. - $f ( x ) = 0.7 ^ { x }$

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. - $\log _ { 6 } ( x + 3 ) = 3$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \sqrt { 11 x }$

Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e } ^ { 7 }$