# Logarithmic Functions

Worksheet that goes along with a gizmo found at explorelearning.com
A logarithmic function is the inverse of an exponential function. When the Gizmotm starts, you will see the graph of a logarithmic function, y = loga(x), and the graph of its associated exponential function, y = ax.
â€¢ With Show associated exponential turned on, use the slider to vary the value of a. In the logarithmic function and in the exponential function, a is called the base.
â€¢ How does the graph of the logarithmic function compare to the graph of the associated exponential function?
â€¢ How do changes in the base affect the graph of the exponential function?
â€¢ How do changes in the base affect the graph of the logarithmic function?
â€¢ Turn on Show line y = x and vary the value of a. How would you describe the relationship between the logarithmic function, the exponential function, and the line y = x?
â€¢ If a point (C1, C2) is part of a function, then the point (C2, C1) is part of the inverse of the function. With Show associated exponential turned on, set a = 5 to graph the logarithmic function y = log5(x) and the exponential function y = 5x. (To quickly set a slider to a specific number, type the number into the field to the right of the slider, and then press ENTER.)
â€¢ Turn on Show probe and drag the probe to find the point (5, 1) on the graph of the logarithmic function. What point must exist on the graph of the associated exponential function? Verify your answer by locating this point on the graph of the exponential function.
â€¢ What is the x-intercept of the logarithmic function? Use the probe to find this value on the graph. How does this intercept relate to the associated exponential function
â€¢ Vary the value of a. In general, what is the x-intercept of the logarithmic function? How does this intercept relate to the associated exponential function?
â€¢ Does the exponential function y = ax have an x-intercept? Does the logarithmic function y = loga(x) have a y-intercept? Why or why not?
â€¢ Graph the function y = log3(x) by setting a = 3. Turn on Show probe, and drag the probe to x = 1.
â€¢ What is the output, or y-value, of this function when x = 1?
â€¢ Vary the value of a and observe the output of the function. What do you notice about the output when x = 1?
â€¢ What can you conclude about the x-intercept of a logarithmic function y = loga(x)?
â€¢ Based on this result, what can you conclude about the y-intercept of the associated exponential function y = ax? Verify this result by turning on Show associated exponential and examining the graph of y = ax as you vary the value of a.
â€¢ Graph the function y = log2(x) by setting a = 2. Turn on Show probe, and drag the probe to see the output of this function for different values of x.
â€¢ What is the output of this function when x = 2, when x = 4, and when x = 8?
â€¢ Based on these output values, what do you think the output will be when x = 16? Use the probe to check your answer.
â€¢ How would you describe the meaning of loga(x)?
â€¢ Is it possible for a to equal 1 in the logarithmic function y = loga(x)? Would the function y = log1(x) have any meaning for an input like x = 4? Why or why not?

# Our Service Charter

1. ### Excellent Quality / 100% Plagiarism-Free

We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions

We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure

We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee

If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.

We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

or