Exam 4: Exponential and Logarithmic Functions

Express as a single logarithm. - $\ln \frac { x ^ { 2 } + 4 x - 32 } { x - 3 } - \ln \frac { x ^ { 2 } + 5 x - 24 } { x + 3 } + \ln \left( x ^ { 2 } - 8 x + 16 \right) , \quad x > 0$

Express as a single logarithm. - $28 \log _ { 7 } \sqrt [ 7 ] { x } + \log _ { 7 } \left( 28 x ^ { 6 } \right) - \log _ { 7 } 28$

Solve the equation. - $2 ^ { x ^ { 2 } - 3 } = 64$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 40 - \log _ { 4 } 10$

The graph of a logarithmic function is shown. Select the function which matches the graph. - A) $y = 3 - \log ( x )$ B) $y = \log ( x - 3 )$ C) $y = \log ( x ) - 3$ D) $y = \log ( 3 - x )$

Graph the function using a graphing utility and the Change-of-Base Formula. - $y = \log _ { 3 } ( x - 2 )$ A) B) C) D)

Graph the function. - $f ( x ) = e ^ { x + 5 }$ A) B) C) D)

Solve the equation. - $\log ( 3 x ) = \log 5 + \log ( x - 4 )$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$

Solve the problem. -The logistic growth model $P ( t ) = \frac { 1,450 } { 1 + 28 e ^ { - 0.313 t } }$ represents the population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population?

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 15$

The graph of an exponential function is given. Match the graph to one of the following functions. - A) $y = 0.65 ^ { x }$ B) $y = 0.32 ^ { x }$ C) $y = 2.4 ^ { x }$ D) $y = 3.5 ^ { x }$

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 5 x + 4 } { 3 }$

Find the domain of the function. - $f ( x ) = \log _ { 1 / 2 } ( x + 4 )$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log \left( 1 - \frac { 1 } { x ^ { 3 } } \right)$

Solve the problem. -The Feldmans bought their first house for $14,000. Over the years they moved three times into bigger and bigger houses. Now, 41 years later, they are ready to retire and want a smaller house like the first one they Bought. If inflation in property values has averaged 3.6% per year during that time, how much will such a House cost them now? (Round your answer to the nearest dollar.)

Express as a single logarithm. - $8 \log _ { b } 8 + 9 \log _ { b } 3$

The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt [ 3 ] { x + 5 }$

Solve the problem. -The logistic growth functi $f ( t ) = \frac { 12,000 } { 1 + 199 e ^ { - 1.7 t } }$ 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 were ill after 9 weeks?