What is the evaluation of log2(8)?
Understand the Problem
The question is asking for the evaluation of the expression log base 2 of 8. This involves using the properties of logarithms to simplify and find the value.
Answer
3
Answer for screen readers
The value of $ \log_2(8) $ is 3.
Steps to Solve
- Identify the Logarithmic Expression
We need to find the value of $ \log_2(8) $.
- Express 8 as a Power of 2
Since 8 can be written as a power of 2, we have:
$$ 8 = 2^3 $$
- Use the Property of Logarithms
Using the property of logarithms, $ \log_b(a^n) = n \cdot \log_b(a) $, we can simplify:
$$ \log_2(8) = \log_2(2^3) $$
- Evaluate the Logarithm
Now we can simplify using the previous property:
$$ \log_2(2^3) = 3 \cdot \log_2(2) $$
Since $ \log_2(2) = 1 $, we find:
$$ 3 \cdot 1 = 3 $$
The value of $ \log_2(8) $ is 3.
More Information
The logarithm represents the exponent to which the base must be raised to produce a certain number. In this case, since $2^3 = 8$, the logarithm evaluates to 3.
Tips
- Misidentifying the Base: Sometimes students confuse the base of the logarithm; ensure you're using the correct base.
- Forgetting Logarithm Properties: It's easy to overlook logarithmic identities, like turning expressions into powers.
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