Question

The value of $x$ which satisfy $log(x+1)=2logx$ is

• A. $1$
• B. $\frac{\sqrt{5}-1}{2}$
• C. $\frac{\sqrt{5}+1}{2}$
• D. $2$

Answer 1

Answer: (B), (C)

The correct options are
B $\frac{\sqrt{5}+1}{2}$
C $\frac{\sqrt{5}-1}{2}$

$\log (x+1)=2\log x$

$\Rightarrow \log (x+1)=\log x^2$

$\Rightarrow x^2-x-1=0$

$\Rightarrow x=\frac{+1\pm \sqrt{1+4}}{2}=\frac{1\pm \sqrt{5}}{2}$

$\Rightarrow x=\left(\frac{1+\sqrt{5}}{2}\right),\left(\frac{1-\sqrt{5}}{2}\right)$