Question

Solve :
$lo{g}_x(x+7)<0$

• A. $(0,1)$
• B. $(-\infty ,1)$
• C. $(-1,0)$
• D. $(-1,1)$

Answer 1

The correct option is A $(0,1)$

$\begin{array}{c}{\log }_x\left(x+7\right)<0\\ forx>1\\ {\log }_x\left(x+7\right)<0\\ \Rightarrow {\alpha }^{x+7}<1\\ \Rightarrow nosolution\\ for0<x<1\\ {\log }_x\left(x+7\right)<0\\ x+7>1\\ x>-6\\ \Rightarrow x\in \left(0,1\right)\end{array}$

Hence,

Option$A$ is correct answer.