Exam 5: Inverse, Exponential, and Logarithmic Functions

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to -The function defined by $f ( x ) = x + 2$ was used to encode a message as: 15 3 22 10 9 7 16 11 23 21 Find the inverse function and determine the message.

Use properties of logarithms to evaluate the expression. -Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the functi $\ln \left( b ^ { 9 } \sqrt [ 4 ] { a } \right)$

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of $g ( x ) = - a ^ { x }$ . Give the domain and range of $g$ . $f(x)=a^{x}$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 4 ^ { x - 1 } - 3$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $x ^ { 2 } + 6 x + 3 = e ^ { x - 1 } + 2$

Write an equivalent expression in exponential form. - $\log _ { 5 } \left( \frac { 1 } { 25 } \right) = - 2$

rite the word or phrase that best completes each statement or answers the question. -Between what two integers does the solution of $\log 8 x = 2.11$ lie?

Find the value. Give an approximation to four decimal places. - $\log 304 + \log 16$

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } \sqrt { 24 }$

Choose the one alternative that best completes the statement or answers the question. -Assume the cost of a car is $\$ 27,000$ . With continuous compounding in effect, find the number of years it would take to double the cost of the car at an annual inflation rate of $9.1 \%$ . Round the answer to the nearest hundredth.

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 2 ^ { x }$ . Find $f ( 4.5 )$ .

Evaluate the logarithm. - $\log _ { 22 } 1$

Solve the equation. - $e ^ { 5 x - 1 } = \left( e ^ { 2 } \right) ^ { - x }$

Solve the equation. Round to the nearest thousandth. - $2 \mathrm { e } ^ { ( 2 x - 3 ) } = 8$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 3 ^ { x }$ . Find $f ( - 2 )$

Solve the equation and express the solution in exact form. - $\log ( 3 + x ) - \log ( x - 4 ) = \log 4$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $e ^ { x } - 13 = - 42 e ^ { - x }$

Decide whether the pair of functions graphed are inverses. -

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 4 ^ { x }$ . Find $\left( \frac { 5 } { 2 } \right)$ .

Graph the function. Give the domain and range. - $f(x)=\log _{1 / 3}(1-x)$