First slide

Theory of equations

Question

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

Moderate

A

$x^{2} + x - e = 0$
B

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

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

$x^{2} + xe - e = 0$

Solution

$\log_{e} x + \log_{e} (1 + x) = 0 \Rightarrow \log_{e} (1 + x) = \log_{e} (\frac{1}{x}) \Rightarrow x (x + 1) = 1 \Rightarrow x^{2} + x - 1 = 0$

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