QuestionWhich of the following is true about the base of a logarithmic function? and and and b : 0 ando b
Studdy Solution
STEP 1
1. The base of a logarithmic function must satisfy certain conditions for the function to be defined.
2. We need to identify the correct conditions for the base .
STEP 2
1. Review the properties of logarithmic functions.
2. Determine the valid range for the base .
3. Identify the correct statement about the base .
STEP 3
Logarithmic functions are defined for positive bases that are not equal to 1. The function is defined for and .
STEP 4
The base must be greater than 0 because logarithms are undefined for non-positive bases. Additionally, cannot be 1 because the logarithm would not be a valid function (it would not be able to distinguish between different values of ).
STEP 5
Given the options, the correct statement about the base is:
- and .
The correct condition for the base of a logarithmic function is:
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