Примеры логарифмы математика

1) log2 5 * log25 8 =
= log2 5 * log(5^2) 2^3 = log2 5 * (1\2 * 3) * log5 2 =3\2 * log2 5 * 1\log2 5 = 3\2
2) log2 (log3 3^(1\16)) =
= log2 ((1\6) * log3 3 = log2 (1\16 * 1) = log2 1\16 = log2 2^(-4) = (-4) * log2 2 = -4
3) log(1\5) (3V3+V2) + log(1\5) (3V3-V2) =
= log(1\5) [(3V3+V2) * (3V3-V2)] =
= log(1\5) [(3V3)^2 - (V2)^2] =
= log(1\5) (27-2) = log(5^(-1)) 25 = 1\(-1) * log5 5^2 = - 2 * log5 5 = -2
4) log(4*2^(1\4)) 16V2 =
= log(2^(2+1\4) 2^(4+1\2) = (4+1\2) * 1\(2+1\4) * log2 2 = 9\2 * 9\4 = 81\8
5) 121^(0,5 * log11 0,25) =
= (11^2)^(log11 (0,25)^(0,5)) =
= 11^(2 * 0,5 * log11 0,25) = 11^(log11 0,25) = 0,25
6) log2 (log3 (2,25) + log3 log2 16) = =>
__ log2 16 = log2 2^4 = 4
__ log3 log2 16 = log3 4
__ (log3 (2,25) + log3 log2 16) = log3 (2,25) + log3 4 = log3 (2,25 * 4) = log3 9 =
= log3 3^2 = 2 * log3 3 = 2 * 1 = 2
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