# How do you solve (log x)^2+ 3 log x - 10 = 0?

$x = 100$ and $x = {10}^{-} 5$

#### Explanation:

From the given:

${\left(\log x\right)}^{2} + 3 \cdot \log x - 10 = 0$

this is a quadratic equation in log x

Let y=log x

then

${y}^{2} + 3 y - 10 = 0$
solve by factoring

$\left(y - 2\right) \left(y + 5\right) = 0$

we have $y = 2$ and $y = - 5$

Therefore

$\log x = 2$

${10}^{2} = x$
$x = 100$
~~~~~~~~~~~~~~
Also $y = - 5$

and $\log x = - 5$

${10}^{-} 5 = x$

$x = \frac{1}{100000} = 0.00001$

$x = 0.00001$

God bless...I hope the explanation is useful