Approximate the logarithm using the properties of logarithms, given logb 2 ≈ 0.3562, logb 3 ≈ 0.5646, and logb 5 ≈ 0.8271. (Round your answer to four decimal places.)

Question

Approximate the logarithm using the properties of logarithms, given log_b 2 ≈ 0.3562,

 log_b 3 ≈ 0.5646, and log_b 5 ≈ 0.8271. (Round your answer to four decimal places.)

log_b 75

Answer 1

log_b75 = log_b[(5²)(3)] = log_b(5²) + log_b3 = 2log_b5 + log_b3 = 2(0.8271) + 0.5646