Logarithmic Functions
In the following problems, determine the logarithmic form or exponential form for the given expression, whichever is appropriate.
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| 1) What is the logarithmic expression for the given exponential expression?
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| 2) What is the logarithmic expression for the given exponential expression?
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| 3) What is the logarithmic expression for the given exponential expression?
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One-to-One Property of Exponents
In the following problems, express the logarithms in exponential form, and apply the one-to-one property of exponents to find the value of x in the equation without using a calculator.
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| 4) Solve for x. |
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| 5) Solve for x.
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Graphs of Logarithmic Functions
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| 8) True or False? The graph is a logarithmic graph.
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| 9) Answer the following questions about the graph of the given logarithmic equation? Check the answer by graphing the parent function and the given function on a calculator or the graphing calculator at this website www.desmos.com. (Note: To make a log entry at this website, click on the Functions button, and then the Calc tab.)
(a) How does the given graph compare to the parent function, y = log5 x ? Explain any changes in shift, compression, and reflection.
(b) What is the domain of the function?
(c) What is the range of the function?
(d) What is the vertical asymptote of the function?
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| 10) Answer the following questions about the graph of the given logarithmic equation? Check the answer by graphing the parent function and the given function on a calculator or the graphing calculator at this website www.desmos.com. (Note: To make a log entry at this website, click on the Functions button, and then the Calc tab.)
(a) How does the given graph compare to the parent function, y = log3 x ? Explain any changes in shift, compression, and reflection.
(b) What is the domain of the function?
(c) What is the range of the function?
(d) What is the vertical asymptote of the function?
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Properties of Logarithmic Functions
In the following problems, state the expression as a single logarithm; and then simplify, if possible.
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| 12) State the expression as a single logarithm. Simplify, if possible.
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| 13) State the expression as a single logarithm. Simplify, if possible.
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| 14) State the expression as a single logarithm. Simplify, if possible.
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In the following problems, state the expression as a sum or a difference of logarithms. Simplify, if possible.
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| 15) State the expression as a sum or a difference of logarithms. Simplify, if possible.
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| 16) State the expression as a sum or a difference of logarithms. Simplify, if possible.
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| 17) State the expression as a sum or a difference of logarithms. Simplify, if possible.
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In the following problems, evaluate the logarithmic expressions by applying the exponential and logarithmic inverse properties.
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In the following problems, solve for x. Check the answers and remember to reject any value of x that produces the logarithm of a negative number or the logarithm of zero.
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Applications of Common Logarithms
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In the following problems, solve the equation for x. Round the answers to the nearest hundredth.
Hint: Take the logarithm of each side of the equation and use the properties of logarithms to solve for x.
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In the following problems, use the change-of-base formula to evaluate the logarithmic expression rounded to the nearest hundredth.
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In the following problems, solve for x by graphing using a graphing calculator or the calculator at this website www.desmos.com. Round the answers to the nearest hundredth.
Solving an Exponential Equation with a Graph
Hint: For each problem, graph two separate equations and find the x coordinate of the point of intersection.
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| 36) Extended Learning
Watch the following video, then write a five-sentence paragraph summarizing the video.
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| 37) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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