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. - $\log _ { 5 } ( 6 x + 5 ) = \log _ { 5 } ( 6 x + 2 )$

Graph the function by making a table of coordinates. - $f(x)=5^{x}$

Use the Power Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 10 ] { x }$

Write the equation in its equivalent logarithmic form. - $72 = 49$

Solve the problem. -The formula $\mathrm { A } = 291 \mathrm { e } ^ { 0.024 \mathrm { t } }$ models the population of a particular city, in thousands, $\mathrm { t }$ years after 1998 . When will the population of the city reach 353 thousand?

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

The graph of a logarithmic function is given. Select the function for the graph from the options. -

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

Graph the function. -Use the graph of $f ( x ) = 5 ^ { x }$ to obtain the graph of $g ( x ) = 5 ^ { x - 4 }$

Find the domain of the logarithmic function. - $f ( x ) = \ln \left( \frac { 1 } { x - 5 } \right)$

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places - $\log _ { 7 } 18$

Solve the problem. -Use the mathematical model for power gain, $G = \log \left( \frac { P _ { 0 } } { P _ { i } } \right) ^ { 10 }$ , where $P _ { 0 }$ is the output power in watts and $P _ { i }$ is the input power in watts. Determine the power gain $\mathrm { G }$ , in decibels, for an amplifier with an output $P _ { 0 }$ of 19 watts and an input $P _ { i }$ of $1.1$ watts. Round to five decimal places if necessary.

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Solve the problem. -Larry has $2200 to invest and needs $2700 in 12 years. What annual rate of return will he need to get in order to accomplish his goal, if interest is compounded continuously? (Round your answer to two Decimals.)

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. - $\log _ { 9 } ( 5 x - 1 ) = \log _ { 9 } ( 2 x + 8 )$

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. - $\log _ { 4 } ( x + 1 ) = 1 + \log _ { 4 } ( x - 4 )$

Use the Quotient Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \left( \frac { x } { 100 } \right)$

Model Exponential Growth and Decay Solve. -The population of a particular country was 23 million in 1981 ; in 1987 , it was 32 million. The exponential growth function $\mathrm { A } = 23 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1981. Use the fact that 6 years after 1981 the population increased by 9 million to find $\mathrm { k }$ to three decimal places.

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

Approximate the number using a calculator. Round your answer to three decimal places. - $\mathrm { e } ^ { 3.2 }$