10^ (4x) - 133*100^x+1000=0.

10 ^ (4x) - 133 * 100 ^ x + 1000 = 0;

10 ^ (4x) - 133 * 10 ^ (2x) + 1000 = 0;

произведем замену 10 ^ (2x) = t;

t ^ 2 - 133t + 1000 = 0;

D = b ^ 2 - 4ac = ( - 133) ^ 2 - 4 * 1 * 1000 = 13689;

t₁ = (133 - sqrt (13689)) / 2 = (133 - 117) / 2 = 8;

t₂ = (133 + sqrt (13689)) / 2 = (133 + 117) / 2 = 125;

10 ^ (2x₁) = 8;

lg2x₁ = lg8;

2x₁=100000000;

x₁ = 50000000;

10 ^ (2x₂) = 125;

lg 2x2 = lg125;

2x₂ = 10 ^ 125;

x₂ = 5 * 10 ^ 124.