6 Questions
What is the inverse function of exponentiation?
Logarithm
What is the base of the natural logarithm?
e
In the logarithmic function y = logₐ(x), what does 'a' represent?
Base
What is the domain of the logarithmic function y = logₐ(x)?
x > 0
In the logarithmic function y = logₐ(x), what is the relationship between 'a' and the base of the natural logarithm?
'a' can be any positive real number, while the base of the natural logarithm is a specific constant.
What happens to the graph of y = logₐ(x) when 'a' is greater than 1?
The graph becomes steeper.
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.
Test your knowledge on logarithmic functions by answering questions about inverse functions, natural logarithms, bases, domains, and the effects of changing the base on the graph.
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