Exam 4: Exponential and Logarithmic Functions

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations 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. - $\log x + \log ( x + 1 ) = \log 56$

Model Exponential Growth and Decay Solve. -The function $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.00693 \mathrm { x } }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. If 700 pounds of the material are placed in the vault, how much time will need to pass for only 231 pounds to remain?

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

Use the Definition of a Logarithm to Solve Logarithmic Equations 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. - $\log _ { 2 } ( x + 4 ) = 3$

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln \sqrt [ 6 ] { \mathrm { e } }$

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. - $8 \ln ( x - 6 ) - 11 \ln x$

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $y = 24 ( 2.1 ) ^ { x }$

Solve the problem. -The function f(x)= 1 + 1.3 ln (x + 1)models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the Basketball player has practiced for two hours. After 217 days of practice, what is the average number of Consecutive free throws the basketball player makes?

Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Find the accumulated value of an investment of $6000 at 7% compounded continuously for 5 years.

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $7 ^ { x } = 13$

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. - $3 \log _ { 6 } x + 5 \log _ { 6 } ( x - 6 )$

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. - $6 \ln x - \frac { 1 } { 4 } \ln y$

Solve the problem. -Find out how long it takes a $\$ 2900$ investment to double if it is invested at $7 \%$ compounded monthly. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

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. - $\frac { 1 } { 7 } \left( \log _ { 4 } x + \log _ { 4 } y \right)$

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. - $\mathrm { y } = 1.5 ( 1.8 ) ^ { \mathrm { x } }$

Use the Definition of a Logarithm to Solve Logarithmic Equations 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. - $\ln x = 8$

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

Evaluate the expression without using a calculator. - $\log _ { 10 } 10$

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations 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. - $2 \log x = \log 100$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { W } \left( \frac { 9 x } { 5 } \right)$