log base 2 of 512
Understand the Problem
The question is asking for the logarithm base 2 of the number 512. This means we need to find the exponent to which 2 must be raised to get 512.
Answer
9
Answer for screen readers
The logarithm base 2 of 512 is $9$.
Steps to Solve
- Express the problem using exponential form
We need to find $x$ such that $2^x = 512$.
- Rewrite 512 as a power of 2
To solve for $x$, let's rewrite 512 in terms of powers of 2. We can do this by factoring 512:
$$ 512 = 2^9 $$
- Set the exponents equal
Now that we know that $512 = 2^9$, we can set the exponents equal to each other:
$$ x = 9 $$
The logarithm base 2 of 512 is $9$.
More Information
The logarithm base 2 of a number gives us the exponent needed to raise 2 to reach that number. In this case, since $2^9 = 512$, we found that the exponent is 9.
Tips
- One common mistake is to miscalculate the powers of 2. Always double-check by multiplying if you're unsure.
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