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Logarithmic Functions Quiz

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Questions and Answers

What is the inverse function of exponentiation?

Addition

Multiplication

Logarithm (correct)

Division

What is the base of the natural logarithm?

e (correct)

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)?

x > 0 Signup and view all the answers

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. Signup and view all the answers

What happens to the graph of y = logₐ(x) when 'a' is greater than 1?

The graph becomes steeper. Signup and view all the answers

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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Description

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.