# How do you solve (Logx)^2 + Log(x^3) + 2 = 0?

Feb 14, 2016

${\left(\log x\right)}^{2} + \log \left({x}^{3}\right) + 2 = 0$

log(a^b)=blog(a)

${\left(\log x\right)}^{2} + 3 \log \left(x\right) + 2 = 0$

This is one expresssion of the type ay^2 +by +c=0

Now we solve the second degree equation:

$\log \left(x\right) = \frac{- 3 \pm \sqrt{{3}^{2} - 4 \cdot 2}}{2}$

$\log \left(x\right) = \frac{- 3 \pm 1}{2}$

$\log \left(x\right) = - \frac{2}{2} \mathmr{and} \log \left(x\right) = - \frac{4}{2}$

$\log \left(x\right) = - 1 \mathmr{and} \log \left(x\right) = - 2$

$x = {e}^{-} 1 \mathmr{and} x = {e}^{-} 2$