Lg(x+1)+lg(x+4)=1 ???

lg((x + 1)(x + 4)) = 1 \\

lg(x^2 + 5x + 4) = 1" alt="lg(x + 1) + lg(x + 4) = 1 \\

lg((x + 1)(x + 4)) = 1 \\

lg(x^2 + 5x + 4) = 1" align="absmiddle" class="latex-formula">

Потенциируем:

x^2 + 5x - 6 = 0 \\

(x + 6)(x - 1) = 0 \\

x_1 = 1 \\

x_2 = -6" alt="x^2 + 5x + 4 = 10^1 = 10 \\

x^2 + 5x - 6 = 0 \\

(x + 6)(x - 1) = 0 \\

x_1 = 1 \\

x_2 = -6" align="absmiddle" class="latex-formula">

$x_2$ не подходит по ОДЗ, следовательно, ответ $x = x_1 = -1$