Explore the limitations of the values of b and x in equations of the form logbx=L by determining which logarithm is undefined.(1 point)
Responses
log2.56.25
logarithm subscript 2.5 baseline 6.25
log1319
logarithm subscript Start Fraction1 over 3 End Fraction baseline Start Fraction 1 over 9 End Fraction
log51
logarithm subscript 5 baseline 1
log50
logarithm subscript 5 baseline 0
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The logarithm is undefined when the base (b) is equal to 1 or less than 0, as logarithms with bases less than or equal to 0 are not defined. Additionally, the argument inside the logarithm (x) must be greater than 0, otherwise the logarithm is undefined.
In the given equations:
1. log2.5(6.25) - The base (2.5) is greater than 1 and the argument (6.25) is also greater than 0, so the logarithm is defined.
2. log13(19) - The base (13) is greater than 1 and the argument (19) is greater than 0, so the logarithm is defined.
3. log5(1) - The base (5) is greater than 1 and the argument (1) is greater than 0, so the logarithm is defined.
4. log5(0) - The base (5) is greater than 1, but the argument (0) is not greater than 0, so the logarithm is undefined.