Is $g(x)=\log x$ convex function? The graph of convex function is :

In a book it is written that $g(x)=\log x$ is strictly convex function. 
So i searched for graph of $g(x)=\log x$ and found that 

Though it has been said that $g(x)=\log x$ is strictly convex function, comparing these two graph it seems to me $g(x)=\log x$ is concave function .
Where am i doing mistake ?

The function is concave if it's second derivative is negative. We have that
$$
g''(x)=(\log(x))''=\biggl(\frac1x\biggr)'=-\frac1{x^2}
$$
for $x>0$. Hence, $g(x)$ is a concave function.
