Question 116
Find the maximum of the function
$$
f(x) = \frac{\lg x \cdot \lg x^{2} + \lg x^{3} + 3}{\lg^{2} x + \lg x^{2} + 2}
$$
and the values of $x$, when it is attained.
$$
f(x) = \frac{\lg x \cdot \lg x^{2} + \lg x^{3} + 3}{\lg^{2} x + \lg x^{2} + 2}
$$
and the values of $x$, when it is attained.