log8 1
Understand the Problem
The question is asking to solve the logarithm of 1 to the base 8. In logarithmic terms, this means we are looking for the exponent to which the base (8) must be raised to produce the number (1). Since any number raised to the power of 0 equals 1, this can be a straightforward calculation.
Answer
$0$
Answer for screen readers
The answer is $0$.
Steps to Solve
- Identify the logarithmic expression
We need to evaluate the logarithm of 1 to the base 8, which is expressed as:
$$ \log_8(1) $$
- Understand the properties of logarithms
A key property of logarithms states that for any base $b$,
$$ \log_b(1) = 0 $$
This is because any number (except 0) raised to the power of 0 equals 1.
- Apply the property to our expression
Using the property we just noted, we can conclude:
$$ \log_8(1) = 0 $$
Thus, the logarithm of 1 to any base, including 8, is always 0.
The answer is $0$.
More Information
This result holds true for any base greater than 0 except for 1, making it a universal property of logarithms. It's an essential concept in understanding how logarithms work in various mathematical contexts.
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