In 3–5 sentences, explain how to approximate log2⋅log3 to four decimal place

Answer 1

To approximate \( \log_2 \log_3 \) to four decimal places, first calculate \( \log_3 \) using the change of base formula: \( \log_3 = \frac{\log_{10}(3)}{\log_{10}(2)} \) or using a scientific calculator. Then, apply the same change of base formula to find \( \log_2 \) of that result: \( \log_2 \log_3 = \frac{\log_{10}(\log_3)}{\log_{10}(2)} \). Finally, round the result to four decimal places for the approximation.