А) lg (4x-3) = 2lg x
ОДЗ:
{4x - 3 >0
{x > 0
{x > 3/4
{x > 0
x > 3/4
lg (4x-3) = 2lg x
lg (4x-3) = lg x^2
4x - 3 = x^2
x^2 - 4x + 3 = 0
D = 16 - 4*1*3 = 4
x1 = (4+2)/2 = 3
x2 = 2/2 = 1
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б) (3^2)^(-3) * 3^(x) = 1
3^(-6) * 3^(x) = 1
3^(x) = 3^(6)
x = 6
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4 + x = sqrt(x + 6)
{4 + x >= 0
{x + 6 >= 0
{x >= -4
{x >= -6
x >= -4
(4 + x)^2 = x + 6
16 + 8x + x^2 = x + 6
x^2 + 7x + 10 = 0
D = 49 - 4*1*10 = 9
x1 = (-7+3)/2 = -4/2 = -2
x2 = -10/2 = -5 - не удовлетворяет ОДЗ