To solve the expression \( \log_2(16) + \log\left(\frac{1}{1000}\right) \), let's break it down into two parts:

### 1. Calculate \( \log_2(16) \):
- The base-2 logarithm of 16 can be expressed as:
  \[
  \log_2(16) = \log_2(2^4)
  \]
- Since \( \log_b(a^c) = c \cdot \log_b(a) \), we get:
  \[
  \log_2(16) = 4 \cdot \log_2(2) = 4 \cdot 1 = 4
  \]

### 2. Calculate \( \log\left(\frac{1}{1000}\right) \):
- The logarithm of a fraction can be calculated as:
  \[
  \log\left(\frac{1}{1000}\right) = \log\left(10^{-3}\right)
  \]
- Using the property \( \log(a^b) = b \cdot \log(a) \), we have:
  \[
  \log\left(10^{-3}\right) = -3 \cdot \log(10)
  \]
- Since \( \log(10) \) in base 10 is 1, we get:
  \[
  \log\left(\frac{1}{1000}\right) = -3 \cdot 1 = -3
  \]

### 3. Add the two results together:
\[
\log_2(16) + \log\left(\frac{1}{1000}\right) = 4 + (-3) = 1
\]

So, the solution is \( \boxed{1} \).

Would you like to dive deeper into logarithmic properties, or do you have any other questions?

Here are 5 related questions to explore further:
1. How would you solve \( \log_2(32) \)?
2. What is the value of \( \log\left(\frac{1}{100}\right) \)?
3. How do logarithm properties apply to solve \( \log_5(25) + \log(100) \)?
4. Can you evaluate \( \log_2(1) \) and explain why it results in that value?
5. What is the inverse function of a logarithm, and how is it used?

**Tip:** Always remember that \( \log_b(1) = 0 \) for any base \( b \) because any number raised to the power of zero is 1.

Learn how to solve the expression log2(16) + log(1/1000) step-by-step. This problem involves properties of logarithms and their applications. Suitable for high school students and anyone interested in logarithmic functions.

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