To solve the equation \(\log_2(x) - \log_2(5) = 4\), we can use properties of logarithms.

First, recall the subtraction rule for logarithms: \(\log_b(A) - \log_b(B) = \log_b\left(\frac{A}{B}\right)\).

Applying this rule, we get:
\[ \log_2\left(\frac{x}{5}\right) = 4 \]

Next, we convert the logarithmic equation to its exponential form:
\[ \frac{x}{5} = 2^4 \]

Since \(2^4 = 16\), the equation becomes:
\[ \frac{x}{5} = 16 \]

To solve for \(x\), multiply both sides by 5:
\[ x = 16 \times 5 \]
\[ x = 80 \]

Therefore, the solution is:
\[ x = 80 \]

Would you like details or have any questions about this solution? Here are some related questions to consider:

1. What is the general rule for converting between logarithmic and exponential forms?
2. How do you solve logarithmic equations with different bases?
3. Can you explain other properties of logarithms used in solving equations?
4. What are the common mistakes to avoid when working with logarithms?
5. How do you apply logarithmic properties in real-world applications?

**Tip:** When solving logarithmic equations, always remember to check if the solution is within the domain of the logarithmic function (i.e., the argument must be positive).

Understand how to solve the logarithmic equation log_2(x) - log_2(5) = 4 using properties of logarithms and exponential functions. This problem focuses on key concepts such as logarithmic subtraction and converting between logarithmic and exponential forms. Suitable for students in Grades 9-11.

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