Mathematics

THE ASSIGNMENTS ARE ON MY BLACKBOARD

Match the graph with its exponential function.

graph of function

y equals 4 to the power of x

y equals minus 4 to the power of minus x end exponent

y equals minus 4 to the power of x

y equals 4 to the power of minus x end exponent

y equals 4 x

Write the logarithmic equation in exponential form.

log subscript 5 25 equals 2

Select the correct rational function for the following graph.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

log subscript 8 fraction numerator x cubed over denominator y cubed z cubed end fraction

3 log subscript 8 x plus 3 log subscript 8 y plus 3 log subscript 8 z

3 log subscript 8 x plus 3 log subscript 8 y minus 3 log subscript 8 z

fraction numerator 3 log subscript 8 x over denominator 3 log subscript 8 y space cross times 3 log subscript 8 z end fraction

3 log subscript 8 x minus 3 log subscript 8 y minus 3 log subscript 8 z

3 log subscript 8 x minus 3 log subscript 8 y plus 3 log subscript 8 z

Solve the exponential equation algebraically. Show all work.

e to the power of minus 4 x squared end exponent equals e to the power of 3 x squared minus 14 x end exponent

Select the correct graph for the given function

y equals 5 plus log open parentheses x plus 2 close parentheses

graph of function

graph of function

graph of function

graph of function

graph of function

Determine whether the statement is true or false. Justify your answer.

The line y equals minus 5 is an asymptote for the graph of f left parenthesis x right parenthesis equals 10 to the power of x minus 5

Solve the equation log open parentheses 1 minus x close parentheses equals log open parentheses 100 close parentheses for x using the One-to-One Property.

-101

-1

The equation has no solution.

-99

101

Condense the expression 3 left parenthesis log x minus log y right parenthesis to the logarithm of a single term.

log x cubed over y

log fraction numerator 3 x over denominator 3 y end fraction

log x over y cubed

3 left parenthesis log x minus log y right parenthesis

log open parentheses x over y close parentheses cubed

Find the exponential model y equals a e to the power of b x end exponent that fits the points shown in the table.

x

0

4

y

5

1

y equals 5 e to the power of minus 0.4024 x end exponent

y equals 5 e to the power of 0.5024 x end exponent

y equals minus 1 fifth e to the power of 0.4024 x end exponent

y equals 1 fifth e to the power of 0.6024 x end exponent

y equals minus 1 fifth e to the power of minus 0.4024 x end exponent

Solve the equation. Round to 3 decimal places.

5 to the power of x equals 8

x=1.415

x=2.292

x=6.724

x=2.526

x=1.292

Identify the graph of the function.

f left parenthesis x right parenthesis equals 3 minus 5 to the power of x

graph of function

graph of function

graph of function

graph of function

graph of function

Write the exponential equation in logarithmic form.

2 cubed equals 8

The population P of a culture of bacteria is described by the equation P left parenthesis t right parenthesis equals 1200 e to the power of 0.052 t end exponent, where t is the time, in hours, relative to the time at which the population was 1200. What was the population at t = 6 hours? Show all work.

Sovle the logarithmic equation algebraically. Approximate the result to three decimal places and show all work.

ln 2x = 3

Determine whether the statement is true or false given that f left parenthesis x right parenthesis equals ln x.

f left parenthesis x minus 7 right parenthesis equals f left parenthesis x right parenthesis minus f left parenthesis 7 right parenthesis comma space x greater than 0

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