Question

1+㏒₃(㏒₃(x+4))>0·························

Answer 1

$1 + log_{3}(log_{3}(x+4))>0 \ \ ODZ: left{ begin{gathered} x + 4 > 0 \ log _{3}(x+4)> 0 \ end{gathered} right. ; left{ begin{gathered} x > -4 \ x > -3 \ end{gathered} right. ; x in(-3;+infty) \ \ log_{3}(log_{3}(x+4)) > log_{3}3^{-1} \ \ log_{3}(x+4) > 3^{-1} \ \ log_{3}(x + 4) > log _{3}3^{frac{1}{3}} \ \ x + 4 > sqrt[3]{3} \ \ x > sqrt[3]{3} - 4$

С учётом ОДЗ (1):

$x in (sqrt[3]{3} -4 ; +infty)$

Ответ: x ∈ (³√3 - 4 ; +∞ )