Algebra 2 7-3 Guided Practice: Logarithmic Functions as Inverses

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Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1.

What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

64
4096
16,777,216
24,287,916

In four different ways
In five different ways
In seven different ways

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Take Note: Write the logarithmic expression that can be read as "log base b of x".

Remember that you can access subscript font using an underscore.

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Take Note: Logarithmic functions and exponential functions are inverses. Complete the statement below that describes their relationship.
\log _bx=y if and only if __________.

Enter an exponential equation that includes b, x, and y.

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Summarize the process of evaluating logarithms by using their exponential form.

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Take Note: What is a common logarithm ?

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Take Note: Provide an example of a common logarithm.

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Problem 3 Got It? In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Approximately how many times more intense was the 1995 earthquake than the 2001 earthquake? Use the Formula in Problem 3.

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Take Note:

Graph the common logarithmic function y=logx at desmos.com.
On the same plane, graph the inverse of that function, the exponential function y=10^{x}.
Graph the linear function y=x to form a diagonal line.
Zoom and pan your graph to establish an appropriate viewing window.
Capture a screenshot of your graph and upload or paste it onto the Formative canvas.
Note that the graphs of the common logarithmic function and the inverse exponential function are reflexive across the diagonal line. Recall that this is a simple visual test to confirm that functions are inverses.

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Problem 4 Got It? What is the graph of y = log4x ? Identify the domain, range, y-intercept, and asymptote(s).

Domain: x > 0
Domain: x > 4
Range: y > 0
Range: all real numbers
y-intercept: 4
No y-intercept
Vertical asymptote: x = 0
No asymptotes

Graph of y=log_4x
Domain of y=\log_4x
Range of y=\log_4x
y-intercept of y=\log_4x
Asymptote(s) of y=\log_4x

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Problem 4 Got It? Reasoning: Suppose you use the table to help you graph y = log2x. 
Recall that if y = log2x, then 2y = x. 
Complete the table.

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Take Note: Consider the general form of transformed logarithmic functions.
Match each type of transformation with its parameter from the general form.

Draggable item		Corresponding Item
horizontal translation (shift)		a
vertical translation (shift)		h
vertical scaling (stretch/compression) & reflection (flip)		k

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Problem 5 Got It? How does the graph of each function compare to the graph of the parent function? Match the appropriate transformation(s) and domain, range, and asymptote changes with each function on the right.

Translate 3 units right
Translate 3 units left
Translate 4 units down
Translate 4 units up
Domain, range, and asymptote remain the same
Domain changes from x > 0 to x > 3
Range remains all real numbers
Asymptote changes from x = 0 to x = 3
Stretch vertically by a factor of 3

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Algebra 2 7-3 Guided Practice: Logarithmic Functions as Inverses

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1. What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Write the logarithmic expression that can be read as "log base b of x".Remember that you can access subscript font using an underscore.

Take Note: Logarithmic functions and exponential functions are inverses. Complete the statement below that describes their relationship. \log _bx=y if and only if __________.Enter an exponential equation that includes b, x, and y.

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of evaluating logarithms by using their exponential form.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What is a common logarithm ?

Take Note: Provide an example of a common logarithm.

Problem 3 Got It? In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Approximately how many times more intense was the 1995 earthquake than the 2001 earthquake? Use the Formula in Problem 3.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 4 Got It? What is the graph of y = log4x ? Identify the domain, range, y-intercept, and asymptote(s).

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider the general form of transformed logarithmic functions. Match each type of transformation with its parameter from the general form.

Problem 5 Got It? How does the graph of each function compare to the graph of the parent function? Match the appropriate transformation(s) and domain, range, and asymptote changes with each function on the right.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1. What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Write the logarithmic expression that can be read as "log base b of x".Remember that you can access subscript font using an underscore.

Take Note: Logarithmic functions and exponential functions are inverses. Complete the statement below that describes their relationship. \log _bx=y if and only if __________.Enter an exponential equation that includes b, x, and y.

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does (as long as a>0)?b^{\log _ba}=a

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does?\log_bb^{a}=a

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of evaluating logarithms by using their exponential form.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What is a common logarithm ?

Take Note: Provide an example of a common logarithm.

Take Note: Which of the following are common logarithms? Select all that apply.

Problem 3 Got It? In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Approximately how many times more intense was the 1995 earthquake than the 2001 earthquake? Use the Formula in Problem 3.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 4 Got It? What is the graph of y = log4x ? Identify the domain, range, y-intercept, and asymptote(s).

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider the general form of transformed logarithmic functions. Match each type of transformation with its parameter from the general form.

Problem 5 Got It? How does the graph of each function compare to the graph of the parent function? Match the appropriate transformation(s) and domain, range, and asymptote changes with each function on the right.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does (as long as a>0)?b^{\log _ba}=a

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does?\log_bb^{a}=a

Take Note: Which of the following are common logarithms? Select all that apply.

Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1.

What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

Take Note: Write the logarithmic expression that can be read as "log base b of x".

Remember that you can access subscript font using an underscore.

Take Note: Logarithmic functions and exponential functions are inverses. Complete the statement below that describes their relationship.
\log _bx=y if and only if __________.

Enter an exponential equation that includes b, x, and y.

Take Note: Consider the general form of transformed logarithmic functions.
Match each type of transformation with its parameter from the general form.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! The chart shows different ways you can write 4 and 16 in the form ab, in which a and b are integers and a ≠ 1.

What is the smallest number you can write in this ab form in four different ways? In five different ways? In seven different ways?

Take Note: Write the logarithmic expression that can be read as "log base b of x".

Remember that you can access subscript font using an underscore.

Take Note: Logarithmic functions and exponential functions are inverses. Complete the statement below that describes their relationship.
\log _bx=y if and only if __________.

Enter an exponential equation that includes b, x, and y.

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does (as long as a>0)?
b^{\log _ba}=a

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does?
\log_bb^{a}=a

Take Note: Consider the general form of transformed logarithmic functions.
Match each type of transformation with its parameter from the general form.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does (as long as a>0)?
b^{\log _ba}=a

Take Note: Explain why the equation below is true. What causes the expression to simplify as it does?
\log_bb^{a}=a