Question

Use the image to answer the question.

A curve is graphed on a coordinate plane. The x-axis ranges from negative 4 to 10 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 1.

Identify a possible base b of this logarithmic function.

(1 point)
Responses

b=14
b equals Start Fraction 1 over 4 End Fraction

b=−4
b equals negative 4

b=0
b equals 0

b=4

Answer 1

To identify a possible base \( b \) of a logarithmic function, we need to consider the properties of logarithms. The base \( b \) must be a positive number that is not equal to 1. This is because logarithms are defined with bases greater than 0 and not equal to 1.

From the provided options:

1. \( b = 14 \) (valid, as it is positive and not equal to 1)
2. \( b = \frac{1}{4} \) (valid, as it is positive and not equal to 1)
3. \( b = -4 \) (invalid, as it's negative)
4. \( b = 0 \) (invalid, as logarithm cannot have a base of 0)
5. \( b = 4 \) (valid, as it is positive and not equal to 1)

From the valid choices, we can conclude that possible bases are \( b = 14 \), \( b = \frac{1}{4} \), and \( b = 4 \). However, when looking at typical logarithmic functions, values greater than 1 are most common, making \( b = 4 \) a strong candidate.

Thus, the possible base \( b \) for the logarithmic function could be:

**b = 4**.