1. Find the value of y. (1) log, 25 = y (2) log3 1 = y (3) 10g16 4 = y (4) 1082 = y (5) log, 1 = y (6) log2 8 = y (7) 10g7 = = y (8) 10g37 = y (9) log 32 = 5 (10) log, y = - 19/ k (11) 10g4 8 = y (12) 1089 81 =y 2. Evaluate. (1) logal (2) log, 4 (3) log, 73 (4) blogs 3 (3) 10g25 53 (4) 161084 8 3. Write the following expressions in terms of logs of a, y and z. (3) log va Vy2 (1) logry (2) log (4) log ry2 2 24 2 (5) log - (6) log (7) log (xy) (8) log IV/2 ar312 ry? (9) log (10) log (11) logry/ VI (12) log Vyz Z4. Write the following equalities in exponential form. (1) log, 81 = 4 (2) log- 7 = 1 (3) 1081 3 =3 (4) log, 1 =0 1 (5) log4 64 = -3 (6) 1086 37 = -2 (7) logy =2 (8) 105m n = 5. Write the following equalities in logarithmic form. (1) 82 = 64 (2) 103 = 10000 (3) 4-2 16 (4) 34 = 81 -5 -3 (5) = 32 (6) = 27 (7) 12 # =y (8) VI = y 6. True or False? (1) log = logx - 3 logy (2) log(a - b) = log a - log b (3) logo* = k . logr (4) (log a) (log b) = log(a + b) log a (5) log b = log(a - b) (6) (Ina)* = k . Ina (7) log a" = a (8) - In = Inc (9) In * = 2k7. Solve the following logarithmic equations. (1) Inc = -3 (2) log(3.x - 2) = 2 (3) 2 logar = log 2 + log(3x - 4) (4) loga + log(x - 1) = log(4x) (5) loga(r + 25) - logs(x - 1) =3 (6) log,(x - 5) + log,(z + 3) = 1 (7) log x + log(x - 3) = 1 (8) log2(x - 2) + log2(r + 1) = 2