Condensing and Expanding Logarithmic Expressions
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the property of logarithms that allows you to condense the expression \(2\log_3u - \log_3z\)?
Back
The property states that \(a\log_b(x) = \log_b(x^a)\) and \(\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)\). Thus, \(2\log_3u - \log_3z = \log_3\left(\frac{u^2}{z}\right)\).
2.
FLASHCARD QUESTION
Front
Convert the logarithmic equation \(\log_x25=3\) into its exponential form.
Back
The exponential form is \(x^3=25\).
Tags
CCSS.HSF.BF.B.5
3.
FLASHCARD QUESTION
Front
How do you expand the logarithmic expression \(\log\left(\frac{x}{y}\right)\)?
Back
Using the property \(\log\left(\frac{a}{b}\right) = \log a - \log b\), the expansion is \(\log x - \log y\).
4.
FLASHCARD QUESTION
Front
What is the condensed form of the expression \(\log_5 7 + 2\log_5 x\)?
Back
Using the properties of logarithms, the condensed form is \(\log_5(7x^2)\).
5.
FLASHCARD QUESTION
Front
How do you condense the expression \(2\log_6a + \log_6b - 3\log c\)?
Back
The condensed form is \(\log_6\left(\frac{a^2b}{c^3}\right)\).
6.
FLASHCARD QUESTION
Front
What is the definition of a logarithm?
Back
A logarithm is the exponent to which a base must be raised to produce a given number. For example, if \(b^y = x\), then \(\log_b x = y\).
Tags
CCSS.HSF.BF.B.5
7.
FLASHCARD QUESTION
Front
What is the change of base formula for logarithms?
Back
The change of base formula states that \(\log_b a = \frac{\log_k a}{\log_k b}\) for any positive base \(k\).
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