Approximate the logarithm using the properties of logarithms

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(2b)^-5

Solution

log_b(2b)^-5

log_b a^m= m log_ba

=-5log_b(2b)

log(mn)=log(m)+log(n)

=-5[log_b2 +log_bb]

=-5[0.3562+1]

=-6.781