12
QuizMultiple Choice

Exponential and Logarithmic Functions — Test

Question 12 • Mathematics III

Which of the following is true about the base b of a logarithmic function?

Answer
A
b is greater than 0 and b is not equal to 1
B
b is greater than 0 and b is equal to 1
C
b is less than 0 and b is equal to 1
D
b is less than 0 and b is not equal to 1

Explanation

For a logarithm with base b to be defined, the base must be positive and cannot equal 1. A base of 1 would make the associated exponential function constant rather than one-to-one, and a negative base is not valid for real logarithms. Therefore, the true statement is that b is greater than 0 and not equal to 1.

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