Логарифмические уравнения. log₅(x+3)=2-log₅(2x+1) log^2₃(x) - 2log₃(3x)-1=0

log₅(x+3)=2-log₅(2x+1)  ==> log₅(x+3)+log₅(2x+1) = 2 ==> (x+3)(2x+1) = 5^2 = 25.

2x^2+7x-22 = 0. x_1 = -11/2, x_2 = 2

0 = log^2₃(x) - 2log₃(3x)-1 = log^2₃(x) - 2log₃(x) -1 - 2log₃(3) = (log₃(x)-1)^2 - 2log₃(3).

2log₃(3) = (log₃(x)-1)^2.

log₃(x) = 1 +-  sqrt(2log₃(3))

x_1 = 3 * e^sqrt(2log₃(3))

x_2 = 3 / e^sqrt(2log₃(3))