Log2 (15*6)

To simplify \(\log_2(15 \times 6)\), you can use the property of logarithms that states: \[ \log_b(m \times n) = \log_b(m) + \log_b(n) \] So, we can rewrite the expression as: \[ \log_2(15 \times 6) = \log_2(15) + \log_2(6) \] Now, if you want to calculate the value numerically, you can use the change of base formula: \[ \log_2(x) = \frac{\log_{10}(x)}{\log_{10}(2)} \] Calculating: 1. \(\log_{10}(15) \approx 1.1761\) 2. \(\log_{10}(6) \approx 0.7781\) 3. \(\log_{10}(2) \approx 0.3010\) So, \[ \log_2(15) \approx \frac{1.1761}{0.3010} \approx 3.905 \] \[ \log_2(6) \approx \frac{0.7781}{0.3010} \approx 2.585 \] Now, adding these values together: \[ \log_2(15 \times 6) \approx 3.905 + 2.585 \approx 6.490 \] Thus, \(\log_2(90) \approx 6.490\).