First slide

Theory of expressions

Question

The number of negative integral values of x satisfying the inequality $\log_{0.6} (\log_{6} \frac{x^{2} + x}{x + 4}) < 0 is$

Moderate

A

0
B

1
C

2
D

Infinite

Solution

$\begin{array}{l} \log_{0.6} (\log_{6} \frac{x^{2} + x}{x + 4}) < 0 \\ \Rightarrow \log_{6} (\frac{x^{2} + x}{x + 4}) > 1 \\ \Rightarrow \frac{x^{2} + x}{x + 4} > 6 \Rightarrow \frac{x^{2} + x}{x + 4} - 6 > 0 \\ \Rightarrow \frac{x^{2} - 5 x - 24}{x + 4} > 0 \end{array}$
$\begin{array}{l} \Rightarrow \frac{(x - 8) (x + 3)}{x + 4} > 0 \\ \Rightarrow x \in (- 4, - 3) \cup (8, \infty) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App