1. log4 2,56+log4 6,25 2. 169^log13 2 3. log0,04(5 40,2) 4.

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 ^ log13 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 * 53)   = 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 * 8b), 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.