Chapter 12/13.2
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Mathematics
•
University
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the property of logarithms that allows you to combine logarithms with the same base?
Back
The properties of logarithms state that \( \log_a b + \log_a c = \log_a (bc) \) and \( \log_a b - \log_a c = \log_a \left( \frac{b}{c} \right) \).
2.
FLASHCARD QUESTION
Front
Convert the logarithmic equation \( \log_{2}8=3 \) to exponential form.
Back
The exponential form is \( 2^3=8 \).
3.
FLASHCARD QUESTION
Front
What is the definition of a one-to-one function?
Back
A function is one-to-one if it never assigns the same value to two different domain elements, meaning if \( f(a) = f(b) \), then \( a = b \).
4.
FLASHCARD QUESTION
Front
How do you express \( 3\log_a6-3\log_a2 \) using properties of logarithms?
Back
This can be expressed as \( 3(\log_a 6 - \log_a 2) = 3\log_a \left( \frac{6}{2} \right) = 3\log_a 3 = \log_a 27 \).
5.
FLASHCARD QUESTION
Front
What is the graph of the function \( f(x)=3^{3x}-1 \) as x approaches infinity?
Back
As \( x \) approaches infinity, \( f(x) \) approaches infinity as well, indicating an exponential growth.
6.
FLASHCARD QUESTION
Front
What is the logarithmic identity for \( \log_a a \)?
Back
The identity states that \( \log_a a = 1 \) for any base \( a \) where \( a > 0 \).
7.
FLASHCARD QUESTION
Front
What is the change of base formula for logarithms?
Back
The change of base formula is given by \( \log_a b = \frac{\log_c b}{\log_c a} \) for any positive base \( c \).
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