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To solve the equation

\[
\log_2 (x - 3) = \log_2 9
\]

we can proceed as follows:

1. Since both sides of the equation have the same base (base 2), we can remove the logarithms and set the arguments equal to each other. This gives:
   \[
   x - 3 = 9
   \]

2. Solving for \( x \), we add 3 to both sides:
   \[
   x = 9 + 3 = 12
   \]

Therefore, the solution is:
\[
x = 12
\]

Would you like further details or have any questions?

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Here are some related questions for further practice:

1. Solve \( \log_5 (x + 4) = \log_5 16 \).
2. Solve \( \log_3 (2x + 1) = \log_3 7 \).
3. Solve \( \log_4 (x - 2) = \log_4 25 \).
4. If \( \log_7 (x - 5) = \log_7 11 \), what is \( x \)?
5. Solve \( \log_8 (3x - 4) = \log_8 10 \).

**Tip:** When solving equations with logarithms of the same base, you can equate the arguments directly if the logs are isolated on both sides.

Solve log_2(x - 3) = log_2 9 algebraically.

Learn how to solve the logarithmic equation log_2(x - 3) = log_2 9 step-by-step. This problem covers key concepts in logarithmic equations, properties of logarithms, and the one-to-one property of logarithms. Suitable for students in Grades 9-11.

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