log2 65536
Understand the Problem
The question is asking for the logarithm base 2 of the number 65536. To solve this, we need to find what power 2 must be raised to in order to equal 65536.
Answer
$16$
Answer for screen readers
The logarithm base 2 of 65536 is $16$.
Steps to Solve
- Identify the logarithmic equation
We want to solve for $x$ in the equation:
$$ 2^x = 65536 $$
- Rewrite 65536 as a power of 2
To find the value of $x$, we need to express 65536 as a power of 2. Let's factor it out:
$$ 65536 = 2^{16} $$
- Equate the powers of 2
Since both sides of the equation are powers of 2, we can set the exponents equal to each other:
$$ x = 16 $$
The logarithm base 2 of 65536 is $16$.
More Information
The answer shows that $65536$ is equal to $2^{16}$. This can also be verified by calculating $2^{16}$ and observing that it equals $65536$. Logarithmic functions are useful in various fields, including computer science and engineering, where binary systems are often used.
Tips
- Forgetting to express 65536 as a power of 2 can lead to incorrect calculations. Always check if the number can be simplified in terms of the base.
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