0,25 * (4^ (5x-16)) = ((√2) / 4) ^-x

0,25 * (4^ (5 * x - 16)) = ((√2) / 4) ^ (-x);

Приведем уравнение к показательному виду.

0.5^2 * (2^ (2 * (5 * x - 16)) = (2^ (1/2) / 2^2) ^ (-x);

(1/2) ^2 * (2^ (2 * (5 * x - 16)) = (2^ (1/2) / 2^2) ^ (-x);

2^ (-1) * (2^ (2 * (5 * x - 16)) = (2^ (1/2 - 2)) ^ (-x);

Упростим.

2^ (-1 + (2 * (5 * x - 16)) = (2^ (-1,5)) ^ (-x);

2^ (-1 + 2 * 5 * x - 2 * 16) = 2^ (1.5 * x);

2^ (-1 + 10 * x - 32) = 2^ (1.5 * x);

2^ (10 * x - 33) = 2^ (1.5 * x);

10 * x - 33 = 1.5 * x;

10 * x - 1.5 * x = 33;

8.5 * x = 33;

x = 33/8.5;

x = 330/85;

x = 66/17.