1) lg (6*5^x-25*20^x) - lg (25) = x2) lg (2^х+х+4) = х-хlg (5)

1.

lg (6 * 5^x - 25 * 20^x) - lg (25) = x;

lg ((6 * 5^x - 25 * 20^x) / 25) = x;

(6 * 5^x - 25 * 20^x) / 25 = 10^x;

6 * 5^x - 25 * 20^x - 25 * 10^x = 0;

6 - 25 * 4^x - 25 * 2^x = 0;

2^x = t;

6 - 25t^2 - 25t = 0;

25t^2 + 25t - 6 = 0;

D = 25^2 + 4 * 6 * 25 = 1225;

t = (-25 ± 35) / 50;

t1 = - 6/5; t2 = 1/5.

1) 2^x = - 6/5 - не имеет решения;

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

x = - log2 (5).

2.

lg (2^х + х + 4) = х - хlg5;

lg (2^х + х + 4) = х (1 - lg5);

lg (2^х + х + 4) = х (lg10 - lg5);

lg (2^х + х + 4) = хlg2;

lg (2^х + х + 4) = lg (2^x);

2^х + х + 4 = 2^x;

х + 4 = 0;

х = - 4.