log_2 1024
Understand the Problem
The question is asking for the logarithm of 1024 to the base 2. This involves determining what power of 2 results in 1024. Since 1024 is a power of 2, we can express it as 2 raised to some exponent.
Answer
$10$
Answer for screen readers
The answer is $10$.
Steps to Solve
- Recognize the logarithmic relationship
The logarithm $ \log_2(1024) $ asks what exponent we need to raise 2 to in order to get 1024.
- Express 1024 as a power of 2
We can express 1024 as a power of 2. We need to factor 1024 to find its base 2 representation: $$ 1024 = 2^{10} $$
- Apply the logarithm rule
Using the property of logarithms that states $ \log_b(b^x) = x $, we can find: $$ \log_2(1024) = \log_2(2^{10}) = 10 $$
- Conclusion with the answer
Therefore, the value of $ \log_2(1024) $ is 10.
The answer is $10$.
More Information
The logarithm indicates the power to which a base number must be raised to produce a given number. In this case, knowing that $1024$ is equal to $2^{10}$ makes it easy to compute the logarithm.
Tips
- Confusing the logarithm with exponentiation. Remember that the logarithm tells you the exponent, not the value you are calculating.
- Forgetting to factor the number correctly to express it as a power of the base.
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