Question

Solve:
$log(1 + x) = 2 log(x)$
​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{log(1+x)=2\,log(x)}$

$\tt{\implies\,log(1+x)=log(x^2)}$

$\tt{\implies\,1+x=x^2}$

$\tt{\implies\,x^2-x-1=0}$

$\tt{\implies\,x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4\cdot(-1)\cdot(1)}}{2\cdot(1)}}$

$\tt{\implies\,x=\dfrac{1\pm\sqrt{1+4}}{2}}$

$\tt{\implies\,x=\dfrac{1\pm\sqrt{5}}{2}}$

$\implies\boxed{\tt{x=\dfrac{1+\sqrt{5}}{2}\,\,\,\,\,\,\,or\,\,\,\,\,\,\,x=\dfrac{1-\sqrt{5}}{2}}}$