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Questions and Answers
What is the exponential form of $log_{32} = -5$?
What is the exponential form of $log_{32} = -5$?
What is the logarithmic form of $16 = 4$?
What is the logarithmic form of $16 = 4$?
Evaluate $log_3 243$.
Evaluate $log_3 243$.
Evaluate $log_{64} 4$.
Evaluate $log_{64} 4$.
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Condense the expression $5 \cdot log_5 4 - log_5 16$ into a single logarithm.
Condense the expression $5 \cdot log_5 4 - log_5 16$ into a single logarithm.
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Condense the expression $2 \cdot log_3 (4k) + 4 \cdot log_3 k$ into a single logarithm.
Condense the expression $2 \cdot log_3 (4k) + 4 \cdot log_3 k$ into a single logarithm.
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Expand the logarithmic expression $log_7 (\frac{m^5}{2})$
Expand the logarithmic expression $log_7 (\frac{m^5}{2})$
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Expand the logarithmic expression $ln(\frac{9a^{16}}{b^2})$ completely.
Expand the logarithmic expression $ln(\frac{9a^{16}}{b^2})$ completely.
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Which expression represents $log_{6} 6$?
Which expression represents $log_{6} 6$?
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Convert $e^{7} = x$ into logarithmic form.
Convert $e^{7} = x$ into logarithmic form.
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Which of the following is equivalent to $log_{2}(8)$?
Which of the following is equivalent to $log_{2}(8)$?
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What is the base of the logarithm in the expression $log_{10} 1000 = 3$?
What is the base of the logarithm in the expression $log_{10} 1000 = 3$?
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Which property can be used to evaluate $log_{3}(81)$?
Which property can be used to evaluate $log_{3}(81)$?
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What is the result of $log_{5}(25) + log_{5}(5)$?
What is the result of $log_{5}(25) + log_{5}(5)$?
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What does $ln(1)$ equal?
What does $ln(1)$ equal?
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Which of the following is a property of logarithms regarding the expression $log_{a}(bcd)$?
Which of the following is a property of logarithms regarding the expression $log_{a}(bcd)$?
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Study Notes
Quiz 4-2: Logarithms
- Convert between exponential and logarithmic forms: Problems 1-4 involve rewriting expressions from logarithmic form to exponential form and vice-versa. Examples include log₂ 32 = −5 and logₓ = 3.
- Evaluate logarithmic expressions: Problems 5-10 involve evaluating logarithms, including using the change of base formula when necessary. Examples include evaluating log₃ 243, log₆ 1, and log₆₄ 4. Questions also include evaluating log₁₂ 3, and ln 60.
- Condense logarithmic expressions: Problems 11-12 involve condensing multiple logarithms into a single logarithm. Examples include problems that simplify expressions like 5·log₄ − log₄ 16 and In 27 + 2·In 8. Also includes condensing expressions like 2 log(4k) + 4 log₃ k and log₄ (9x³/¹⁶) − 2 log₂ (8x³).
- Expand logarithmic expressions: Problems 15-18 involve expanding logarithmic expressions. Examples include problems like log₅ (m³) , log₄ (x³/⁴⁸), ln(p²q), and log(√9a¹⁶/b²).
- Graphing logarithmic functions: Problems 19-20 involve graphing logarithmic functions and identifying key characteristics like domain, range, x-intercepts, asymptotes, intervals where the function is increasing or decreasing, and end behavior. Examples include f(x) = log₅(x − 1) −1 and f(x) = −½•ln(x + 3).
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Description
This quiz focuses on key concepts related to logarithms, including converting between exponential and logarithmic forms, evaluating logarithmic expressions, condensing and expanding logarithmic expressions, and graphing logarithmic functions. Test your understanding of these essential algebraic skills through various problems designed to assess your knowledge.
