Logarithmic Functions and Properties

The video tutorial by Sully covers the manipulation of logarithmic functions, focusing on four key properties: product, quotient, power, and change of base. Each property is explained with examples, demonstrating how to expand and condense logarithmic expressions. The tutorial also explores the graphical implications of these properties, such as vertical shifts and dilations. The change of base formula is highlighted for its practical use in calculators. The session concludes with a graphical interpretation of logarithmic transformations.

What is the product property of logarithms used for?

• To subtract two logarithms

• To divide two logarithms

• To change the base of a logarithm

• To expand the logarithm of a product into a sum

How can the quotient property of logarithms be described?

• It allows the addition of two logarithms

• It allows the multiplication of two logarithms

• It allows the division of a logarithm into a difference

• It changes the base of a logarithm

What does the power property of logarithms state?

• An exponent can be moved to the front as a multiplier

• A logarithm can be added to its base

• A logarithm can be subtracted from its base

• A logarithm can be divided by its base

Which property allows the expression of a logarithm as a single term?

• Change of base formula

• Power property

• Quotient property

• Product property

What is the result of applying the power property to a logarithm with an exponent?

• The exponent is added to the base

• The exponent is subtracted from the base

• The exponent is multiplied with the logarithm

• The exponent is divided by the base

What is the purpose of the change of base formula?

• To subtract two logarithms

• To calculate logarithms with different bases using common or natural logs

• To add two logarithms

• To multiply two logarithms

How does the change of base formula help when using calculators?

• It simplifies the addition of logarithms

• It enables the use of common or natural logs to calculate other bases

• It changes the logarithm into a fraction

• It allows for the multiplication of logarithms

What happens to a graph when a logarithm is expanded using the product property?

• The graph remains unchanged

• The graph shifts vertically

• The graph rotates

• The graph shifts horizontally

How does a vertical dilation affect the graph of a logarithmic function?

• It shifts the graph horizontally

• It rotates the graph

• It compresses the graph vertically

• It expands the graph vertically

What is the effect of a horizontal reflection on a logarithmic graph?

• The graph flips over the y-axis

• The graph shifts up

• The graph flips over the x-axis

• The graph shifts down