Question

Use Laws of Logarithms to solve the following equations. a) Write the expression as a sum, difference or product of logs. Ipa 7 logo b) Write the expression as a single log. (log3 p – log3 9) + 2 logz r c) Solve the equation and give the answer to four decimal places. 31-2x = 4* d) Solve the log equation and give the answer to four decimal places. log(9x) = 2 – log.(x + 3)

Answer 1

едa ! Гр4, 1 а (P1)'2 6 2 6 6 ® (va, P- ангva s” = log Pja) + loggen log (pp са (РФ) [log pq - log (Р°/4 1 2 [+] GP +]. 9-361) & log op + 4 Log 62-22 logot improlent formula: y log a MN = loqa M +44 у од 4 loga M-log an у •4x4 - Ho4 - т

31-2x = 4x 31.322_AZ 介介 42 = 3 -22 3 > >> x=3 > 322 42 E a = 2 → 131334.44=3 (: Qmj"- amn] (6x4) & 3 [:amlam=@bym] (36) Taking logo on both side degel log (36) log 3 7 nog (36) = log 3 x = log 0.3066 Cfour decimal places) log 3/19936² 9 0.3065735 n = 10.3066 10 log 6 (92) = 2-logo (2+3) * loy. Cax)+log,(0+3) = 2 (..- log MtlogNo= log ung loy 1629(X+3)} = 2 [from the definition of "Tog' if log M=x 77 92 (K + 3) = 62 then Maak > 2 - ² x +34-450 Here, M=9*(X+3) 2017 4x-x-1=0 a = 6, 2-2 x(x +4 -1(3+4)=0 (x+4) (-1) =0 .; X=-4 ai u = 1 Herre x=-4 does not satisfy the above 'logo equation . Hence, the solution is a = 1