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Questions and Answers
What is the exponential form of $log_{32} = -5$?
What is the exponential form of $log_{32} = -5$?
- $(-5)^{32} = 1$
- $32^{-5} = x$ (correct)
- $32^{-5} = 1$
- $32^1 = -5$
What is the logarithmic form of $16 = 4$?
What is the logarithmic form of $16 = 4$?
- $log_4 16 = 2$ (correct)
- $log_4 2 = 16$
- $log_{16} 4 = 2$
- $log_2 16 = 4$
Evaluate $log_3 243$.
Evaluate $log_3 243$.
- 5 (correct)
- 81
- 3
- 243
Evaluate $log_{64} 4$.
Evaluate $log_{64} 4$.
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.
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.
Expand the logarithmic expression $log_7 (\frac{m^5}{2})$
Expand the logarithmic expression $log_7 (\frac{m^5}{2})$
Expand the logarithmic expression $ln(\frac{9a^{16}}{b^2})$ completely.
Expand the logarithmic expression $ln(\frac{9a^{16}}{b^2})$ completely.
Which expression represents $log_{6} 6$?
Which expression represents $log_{6} 6$?
Convert $e^{7} = x$ into logarithmic form.
Convert $e^{7} = x$ into logarithmic form.
Which of the following is equivalent to $log_{2}(8)$?
Which of the following is equivalent to $log_{2}(8)$?
What is the base of the logarithm in the expression $log_{10} 1000 = 3$?
What is the base of the logarithm in the expression $log_{10} 1000 = 3$?
Which property can be used to evaluate $log_{3}(81)$?
Which property can be used to evaluate $log_{3}(81)$?
What is the result of $log_{5}(25) + log_{5}(5)$?
What is the result of $log_{5}(25) + log_{5}(5)$?
What does $ln(1)$ equal?
What does $ln(1)$ equal?
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 $log_{a}(bcd)$?
Flashcards
Express 1/32 = 2^-5 in logarithmic form
Express 1/32 = 2^-5 in logarithmic form
The base is 2, the exponent is -5, and the result is 1/32.
Express x^3 = x in logarithmic form
Express x^3 = x in logarithmic form
The base is x, the exponent is 3, and the result is x^3.
Express 16 = 4^2 in logarithmic form.
Express 16 = 4^2 in logarithmic form.
The base is 4, the exponent is 2, and the result is 16.
Express e^7 = x in logarithmic form
Express e^7 = x in logarithmic form
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Evaluate log3(243)
Evaluate log3(243)
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Evaluate log12(1728)
Evaluate log12(1728)
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Condense 5 * log5(4) - log5(16) into a single logarithm
Condense 5 * log5(4) - log5(16) into a single logarithm
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What type of function describes exponential growth or exponential decay?
What type of function describes exponential growth or exponential decay?
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What does the constant 'a' represent in an exponential function of the form y = a * b^x ?
What does the constant 'a' represent in an exponential function of the form y = a * b^x ?
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What does the constant 'b' represent in an exponential function of the form y = a * b^x ?
What does the constant 'b' represent in an exponential function of the form y = a * b^x ?
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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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