Section 7.5: Review & Assessment

This section provides review exercises and assessment questions covering all topics of logarithms, including laws, equations, and applications.

Example 1: Applying Logarithm Laws

Simplify \( \log_2 8 + \log_2 4 \).

Step 1: Use product rule: \( \log_2 8 + \log_2 4 = \log_2 (8 \cdot 4) \)

Step 2: Multiply: \( 8 \cdot 4 = 32 \)

Step 3: Evaluate: \( \log_2 32 = 5 \)

Example 2: Solving Logarithmic Equation

Solve for x: \( \log_3(x-1) = 2 \)

Step 1: Rewrite in exponential form: \( x-1 = 3^2 \)

Step 2: Simplify: \( x-1 = 9 \)

Step 3: Solve: \( x = 10 \)

Practice Problems

  1. Simplify \( \log_5 25 - \log_5 5 \)
  2. Solve \( \log_4 (x+3) = 3 \) for x
  3. Evaluate \( \log_2 16 - \log_2 4 + \log_2 2 \)
  4. Solve \( \log_7 x + \log_7 2 = 3 \) for x
  5. Word Problem: The intensity of sound doubles. By what amount does \( \log I \) change?
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