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 2/5}

Answer 1

One of the properties of logarithms is that when given LOG(b/a) it can be rewritten as LOG(b) - LOG(a)

So your log_b(2/5) can be re-written as log_b(2) - log_b(5). Then you can use the approximation given

to find the answer.

log_b(2) ≈ 0.3562 and log_b(5) ≈ 0.8271

Subtract these and find the answer is approximately -0.4709