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Questions and Answers
What is the value of $log_{10}(1000)$?
What is the value of $log_{10}(1000)$?
- 10
- 3 (correct)
- 100
- 2
Which property of logarithms is represented by the equation $log_b(xy) = log_b(x) + log_b(y)$?
Which property of logarithms is represented by the equation $log_b(xy) = log_b(x) + log_b(y)$?
- Quotient Rule
- Product Rule (correct)
- Power Rule
- Change of Base Formula
If $log_a(b) = c$, what is the equivalent exponential form?
If $log_a(b) = c$, what is the equivalent exponential form?
- a^c = b (correct)
- b^a = c
- c^b = a
- a^b = c
What is the value of $log_{2}(16)$?
What is the value of $log_{2}(16)$?
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For which value of $x$ is $log_{3}(x) = -2$ true?
For which value of $x$ is $log_{3}(x) = -2$ true?
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Study Notes
Logarithmic Values and Properties
- The value of ( \log_{10}(1000) ) is 3, as ( 1000 = 10^3 ).
- The equation ( \log_b(xy) = \log_b(x) + \log_b(y) ) represents the product property of logarithms, which states that the logarithm of a product is the sum of the logarithms of the factors.
Exponential Form
- If ( \log_a(b) = c ), the equivalent exponential form is ( a^c = b ), referring to the relationship between logarithms and exponents.
Specific Logarithmic Values
- The value of ( \log_{2}(16) ) is 4, since ( 16 = 2^4 ).
Solving Logarithmic Equations
- For the equation ( \log_{3}(x) = -2 ), the solution is ( x = \frac{1}{9} ), as ( 3^{-2} = \frac{1}{9} ).
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