Finding the zeroes of a function

Hi,

I'd really appreciate some pointers on how to find the zeroes of the function $\displaystyle f(x)=\frac{x^2}{2}+\log(x)$,

that is, $\displaystyle x \in <0,+\infty>$ for which $\displaystyle \frac{x^2}{2}+\log(x)=0$.

I tried something along the lines of

$\displaystyle \frac{x^2}{2}+\log(x)=0$

$\displaystyle x^2+2\log(x)=0$

$\displaystyle x^2+\log(x^2)=0$

$\displaystyle \log(e^{x^2})+\log(x^2)=0$

$\displaystyle \log(e^{x^2} \cdot x^2)=0$

$\displaystyle e^{x^2} \cdot x^2=1$

but don't really know how to proceed from that.

Many thanks!