Wiedząc że:a) [latex]log _{5} 4=a i log _{5}27=b, oblicz log _{5} 108 oraz log _{5} frac{27}{64} [/latex]b) [latex]log _{4} 3=a i log _{4} 5 =b, oblicz log _{4} 0,6 oraz log _{4} 5 frac{2}{5} [/latex]

a) log₅ 4 = a log₅ 27 = b log₅ 108 = log₅ (4·27) = log₅ 4 + log₅ 27 = a + b log₅ 27/64 = log₅ 27 - log₅ 64 = log₅ 27 - log₅ 4³ = log₅ 27 - 3 log₅ 4 = b - 3a b) log₄ 3 = a log₄ 5 = b log₄ 0,6 = log₄ 6/10 = log₄ 3/5 = log₄ 3 - log₄ 5 = a - b log₄ 5 2/5 = log₄ 27/5 = log₄ 27 - log₄ 5 = log₄ 3³ - log₄ 5 = 3 log₄ 3 - log₄ 5 = 3a - b