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What is the base of the logarithm if log_b(1) = 0?
What is the base of the logarithm if log_b(1) = 0?
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Q1
What is the base of the logarithm if log_b(1) = 0?
Any positive number
1
0
Undefined
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For any base b > 0, log_b(1) = 0, since b^0 = 1.
Questions & Step-by-step Solutions
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Q
Q: What is the base of the logarithm if log_b(1) = 0?
Solution:
For any base b > 0, log_b(1) = 0, since b^0 = 1.
Steps: 4
Show Steps
Step 1: Understand what a logarithm is. A logarithm log_b(x) answers the question: 'To what power must we raise b to get x?'
Step 2: In the equation log_b(1) = 0, we are trying to find the base b such that when we raise b to the power of 0, we get 1.
Step 3: Recall the property of exponents: any number raised to the power of 0 equals 1. This means b^0 = 1 for any base b that is greater than 0.
Step 4: Since log_b(1) = 0 holds true for any base b > 0, we conclude that the base of the logarithm can be any positive number.
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