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Questions and Answers
What is the inverse function of exponentiation?
What is the inverse function of exponentiation?
- Addition
- Multiplication
- Logarithm (correct)
- Division
What is the base of the natural logarithm?
What is the base of the natural logarithm?
- π
- e (correct)
- 2
- 10
In the logarithmic function y = logₐ(x), what does 'a' represent?
In the logarithmic function y = logₐ(x), what does 'a' represent?
- Variable
- Coefficient
- Exponent
- Base (correct)
What is the domain of the logarithmic function y = logₐ(x)?
What is the domain of the logarithmic function y = logₐ(x)?
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In the logarithmic function y = logₐ(x), what is the relationship between 'a' and the base of the natural logarithm?
In the logarithmic function y = logₐ(x), what is the relationship between 'a' and the base of the natural logarithm?
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What happens to the graph of y = logₐ(x) when 'a' is greater than 1?
What happens to the graph of y = logₐ(x) when 'a' is greater than 1?
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Study Notes
Inverse Function of Exponentiation
- The inverse function of exponentiation is the logarithmic function.
Logarithmic Function
- The base of the natural logarithm is 'e', approximately 2.718.
- In the logarithmic function y = logₐ(x), 'a' represents the base of the logarithm.
Domain of Logarithmic Function
- The domain of the logarithmic function y = logₐ(x) is all positive real numbers.
Relationship between 'a' and the Base of the Natural Logarithm
- There is no specific relationship between 'a' and the base of the natural logarithm, as 'a' can be any positive real number except 1.
Graph of Logarithmic Function
- When 'a' is greater than 1, the graph of y = logₐ(x) opens upwards, and the function is increasing.
- When 'a' is between 0 and 1, the graph of y = logₐ(x) opens downwards, and the function is decreasing.
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