log6 1
Understand the Problem
The question is asking to evaluate the logarithm of 1 with a base of 6. Since logarithms answer the question, 'to what power must the base be raised to produce a given number?', here we're looking for the power to which 6 must be raised to yield 1.
Answer
\( \log_6(1) = 0 \)
Answer for screen readers
The answer is ( \log_6(1) = 0 ).
Steps to Solve
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Understanding Logarithmic Identity
Logarithms have a specific property: for any base ( b ), the logarithm of 1 is always 0. This is because any number raised to the power of 0 equals 1. -
Applying the Property
Here, we have a logarithm with base 6. Thus, we can use the property of logarithms: $$ \log_6(1) = 0 $$ -
Final Statement
We conclude that for base 6, the logarithm of 1 is: $$ \log_6(1) = 0 $$
The answer is ( \log_6(1) = 0 ).
More Information
This result comes from the fundamental property of logarithms. Since any base raised to the power of zero equals one, this makes the logarithm of one always zero, regardless of the base used.
Tips
- Confusing properties of logarithms: Sometimes, students may confuse logarithms with exponential functions, leading them to think that ( \log_b(1) ) could be something other than 0. Remembering that any base to the power of 0 is 1 can help avoid this mistake.
