Exercise 3.3.7 solution

  1. \(\log_b ( 6 ) = \log_b ( 2 ) + \log_b ( 3 ) = 1.7095 + 2.7095 = 4.4190\)
  2. \(\log_b ( 72 ) = \log_b ( 2 \cdot 6^2 ) = \log_b ( 2 ) + 2 \log_b ( 6 ) = 10.5475\)
  3. \(\log_b ( 1.5 ) = \log_b ( \frac{3}{2} ) = \log_b ( 3 ) - \log_b ( 2 ) = 1.0000\)
  4. Since \(\log_b ( 1.5 ) = 1\), then \(b^1 = 1.5\). So \(b = 1.5\).