AP PreCalculus Flashcards: Logarithmic Function Manipulation
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What is the product property for logarithms?
The product property states that the logarithm of a product is the sum of the logarithms of its factors: log_{b}(xy) = log_{b}x + log_{b}y.
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What is the product property for logarithms?
The product property states that the logarithm of a product is the sum of the logarithms of its factors: log_{b}(xy) = log_{b}x + log_{b}y.
What does the change of base property imply about the relationship between all logarithmic functions?
This property implies that all logarithmic functions, regardless of their base, are simply vertical dilations (stretches or compressions) of each other.
What is the graphical implication of the power property for logarithms?
Graphically, this property implies that raising the input of a logarithmic function to a power is equivalent to a vertical dilation of the function's graph.
What is the power property for logarithms?
The power property states that the logarithm of a number raised to a power is the product of the power and the logarithm of the number: log_{b}x^{n} = n log_{b}x.
Using the power property, how can you rewrite the expression log_{5}x^{3}?
Using the power property, log_{5}x^{3} can be rewritten as 3 log_{5}x.
What is the change of base property for logarithms?
The change of base property states that a logarithm with any base can be expressed in terms of logarithms with a different base: log_{b}x = log_{a}x / log_{a}b.
How could you use the change of base property to evaluate log_{4}16 using base 2?
Using the change of base property, you can rewrite the expression as log_{2}16 / log_{2}4, which evaluates to 4 / 2 = 2.
Define the natural logarithm, f(x) = ln x.
The function f(x) = ln x is a logarithmic function with the natural base e, meaning that ln x is equivalent to log_{e}x.
Using the product property, how can you expand the expression log_{b}(7a)?
Using the product property, the expression log_{b}(7a) can be expanded into the equivalent form log_{b}7 + log_{b}a.
Which logarithmic property explains why the graph of y=log(x^3) is a vertical stretch of the graph of y=log(x)?
The power property explains this, as log(x^3) is equivalent to 3log(x), which represents a vertical dilation of the parent function by a factor of 3.
What is the graphical implication of the product property for logarithms?
Graphically, the product property implies that every horizontal dilation of a logarithmic function is equivalent to a vertical translation.