The equation _e x + _e (1 + x) = 0 can be written as - Vidyadip

MCQ

The equation ${\log _e}x + {\log _e}(1 + x) = 0$ can be written as

A
${x^2} + x - e = 0$
✓
${x^2} + x - 1 = 0$
C
${x^2} + x + 1 = 0$
D
${x^2} + xe - e = 0$

✓

Answer

Correct option: B.

${x^2} + x - 1 = 0$

b
(b) ${\log _e}x + {\log _e}(1 + x) = 0$ $⇒$ ${\log _e}(1 + x) = {\log _e}\left( {\frac{1}{x}} \right)$

$⇒$ $x(x + 1) = 1\,\, \Rightarrow \,\,{x^2} + x - 1 = 0$

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