1) 2^2x + 14 * 2^x-1 - 29 = 0 2) LOG^6 (X-2) + LOG^6 (X-1) = 13) log^3 8 / log^3 2

1) 2^ (2x) + 14 * 2^ (x - 1) - 29 = 0;

2^ (2x) + 7 * 2^x - 29 = 0; D = 7^2 + 4 * 29 = 49 + 116 = 165; 2^x = (-7 ± √165) / 2;

a) 2^x = (-7 - √165) / 2 < 0 - нет решений;

b) 2^x = (-7 + √165) / 2;

x = log2 (√165 - 7) / 2.

2) log6 (x - 2) + log6 (x - 1) = 1;

{x - 2 > 0;

{x - 1 > 0;

{log6 ((x - 2) (x - 1)) = log6 (6); {x > 2;

{x > 1;

{ (x - 2) (x - 1) = 6; {x > 2;

{x^2 - 3x - 4 = 0; D = 3^2 + 4 * 4 = 25 = 5^2; x = (3 ± 5) / 2; x1 = (3 - 5) / 2 = - 2/2 = - 1; x2 = (3 + 5) / 2 = 8/2 = 4; {x > 2;

{x = - 1; 4; x = 4.

3) Переход к другому основанию:

loga (b) = logc (b) / logc (a); log3 (8) / log3 (2) = log2 (8) = 3.