1. a)log₂8 + log½4 + log₉81 3+(-2)+2=3 b)log 0,1 + log 1000 + log0,1 10 -1+3+(-1)=-2+3=1 c)log₃27 - log₄2 - log₂ 1/8 3-1/2-(-3)=5 1/2 d)log₃₆6 + log₁₆4 - log₈2 1/2+1/2-1/3=2/3 2. Z własności logarytmów o tych samych podstawach (np. log₆ a + log ₆b = log ₆(a*b) ) a)log₆2 + log₆18 log₆(2*18)=log₆36=2 b)log 15 - log 3/2 log (15:3/2)= log 10=1 c)log₆4 +log₆27 - log₆3 log₆(4*27)-log₆3 log₆108-log₆3 log₆(108:3)=log₆36=2 d)log 1/2 - log 25 - log 2 log(1/2:25)-log2 log 1/50 - log2 log(1/50 : 2)=log 1/100=-2
1. logg₂8 + log½4 + log₉81 = log₂ 2³ + log½ (1/2)^-2 + log₉ 9² = 3 + (-2) + 2 = 3 b) log 0,1 + log 1000 + log0,1 10 = log 10^(-1) + log 10³ + log0,1 0,1^(-1) = -1 + 3 + (-1) = 1 c) log₃27 - log₄2 - log₂ 1/8 = log₃ 3³ - log₄ 4^(1/2) - log₂ 2^(-3) = 3 - 1/2 - (-3) = 2,5 + 3 = 5,5 d) log₃₆6 + log₁₆4 - log₈2 = log₃₆ 36^(1/2) + log₁₆ 16^(1/2) - log₈ 8^(1/3) = 1/2 + 1/2 - 1/3 = 2/3 2. a) log₆2 + log₆18 = log₆ (2 * 18) = log₆ 36 log₆ 6² = 2 b) log 15 - log 3/2 = log (15 : 3/2) = log (15 * 2/3) = log 10 = 1 c) log₆4 +log₆27 - log₆3 =log₆(4 * 27) - log₆3 =log₆108 - log₆3 =log₆(108 : 3)=log₆ 36= log₆ 6² =2 d) log 1/2 - log 25 - log 2 = log(1/2 : 25) - log 2 = log(1/2 * 1/25) - log 2 = log (1/50 : 2) = log (1/50 * 1/2) = log 1/100 = log 10^(-2) = -2
1.Obicz: a) log3 243 b) log1/2 32 c) log 1000 d) log2/3 81/16 e) log2 1/1024 f) log1/6 216 g) log5 625 h) log1/5 1 2.Oblicz: a) log0,1 0,01 b) log1,1 1,331 c) log0,64 0,8 d) log0,125 0,5 e) log0,16 0,064 f) log0,2 625 g) log0,0016 5 h) log4 0,0...
