Question

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. log2 (**»*)- 0

Answer 1

li) log, ( xy) Since, logo ( 3 ) = loga a + logaß, therefore, log, (4 xy?) log, 1 + log, x + log, y3 4 log, 1 - log, 4 + log, x + log,y? n loga a log, 1 = 0 Also, log an 2 = - log, 2 + log, x + 3 log, y - 2 10g, 2 + log, I + 3 log, y 2 + log, x + 3 log, y Since, loga a 1. (ii) Hence, 1082 (4 xy?) = -2 + log, 2 + 31082y. i in l vom P23 In( mn) – In (pq?) Since, log.(m) = log, a – logo In(mn) – (Inp + Inq?) Since, loga = n loga a and log(aB) = 109, + logo (In m+ ln n)- + In n) - Inp – 3 Iną. n

Hence, In &mn pa? 1 Inmt 3 Inn - Inp - 3 Inq. (iiil nloga 2 logs m - blogs n blogs n - 4 1085 P Since, logan 2 10gsm 6 logon 4 10gs p = logs m2 - (logs no + logs pt) therefore, log m² -logg no logs 17 P 2 S

soo 4logsp logs (nopt) loga a + loga B = loga aß 2 logs m - 6logen logs And, log, * - loga B = log.com 2 logs m - 6 logan - 4 1095P 4 logs p = logs hop4 Thus, 2 m