Cho \({{\log }_{b}}\left( a+1 \right)>0\), khi...

A

- Hướng dẫn giải

Phương pháp giải:

\({\log _a}f\left( x \right) > {\log _a}g\left( x \right) \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}a > 1\\f\left( x \right) > g\left( x \right)\end{array} \right.\\\left\{ \begin{array}{l}0 < a < 1\\f\left( x \right) < g\left( x \right)\end{array} \right.\end{array} \right.\)

Giải chi tiết:

ĐK: \(0<b\ne 1;\,\,a>-1\)

\({\log _b}\left( {a + 1} \right) > 0 = {\log _b}1 \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}b > 1\\a + 1 > 1\end{array} \right.\\\left\{ \begin{array}{l}0 < b < 1\\a + 1 < 1\end{array} \right.\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}b > 1\\a > 0\end{array} \right.\\\left\{ \begin{array}{l}0 < b < 1\\a < 0\end{array} \right.\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}b - 1 > 0\\a > 0\end{array} \right.\\\left\{ \begin{array}{l}b - 1 < 0\\a < 0\end{array} \right.\end{array} \right. \Rightarrow a\left( {b - 1} \right) > 0\)

Chọn A.