Question

Решите логарифмическое неравенство Log6(2x+4)<2

Answer 1

$\log_6(2x+4)\ \textless \ 2\\\begin{cases}2x+4\ \textless \ 6^2\\2x+4\ \textgreater \ 0\end{cases}\Rightarrow\begin{cases}2x+4\ \textless \ 36\\2x\ \textgreater \ -4\end{cases}\Rightarrow\begin{cases}2x\ \textless \ 32\\x\ \textgreater \ -2\end{cases}\Rightarrow\begin{cases}x\ \textless \ 16\\x\ \textgreater \ -2\end{cases}\\x\in(-2;\;17)$