1. log4 2,56+log4 6,25 2. 169^log√13 2 3. log0,04 (5 4√0,2) 4. log2,5log27 (3 5√3) 5. loga√a^3 8√b, если b^5-a^4=0

Question

Андрей Толкачев

Математика

9 июня, 05:00

1. log4 2,56+log4 6,25 2. 169^log√13 2 3. log0,04 (5 4√0,2) 4. log2,5log27 (3 5√3) 5. loga√a^3 8√b, если b^5-a^4=0

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Роксалана · Answer 1

Найдем значения выражений:

1. log4 2,56 + log4 6,25 = log4 1.6 ^ 2 + log4 2.5 ^ 2 = log2 ^ 2 1.6 ^ 2 + log2 ^ 2 2.5 ^ 2 = 2/2 * log2 1.6 + 2/2 * log2 2.5 = log2 1.6 + log2 2.5 = log2 (1.6 * 2.5) = log2 4 = log2 (2 ^ 2) = 2 * log2 2 = 2 * 1 = 2;

2. 169 ^ log√13 2 = 169 ^ (1/0.5) * log13 2) = 169 ^ (2 * log13 2) = 169 ^ (log13 4) = (13 ^ 2) ^ (log13 4) = 13 ^ (log13 4 ^ 2) = 4 ^ 2 = 16;

3. log0,04 (5 * 0,2 ^ (1/4)) = log0.2 ^ 2 (5 * 1/5 ^ (1/4)) = 1/2 * log0.2 (0.2 ^ ( - 3/4)) = 1/2 * ( - 3/4) = - 3/8;

4. log2,5 log27 (3 * 5√3) = log2,5 log27 (3 * 3 ^ (1/3)) = log2,5 * 1/3 * log27 (3 ^ (6/5)) = log2,5 * (1/3 * 6/5) = log (5/2) * (2/5) = - 1;

5. loga (a ^ 3 * 8√b), если b ^ 5 - a ^ 4 = 0;

loga (a ^ 3 * b ^ (1/8)) = 3 * 1/8 * loga b = 3/8 * loga a ^ (4/5) = 3/8 * 4/5 = 3/10 = 0.3.