log(x + 1) log(x + 2) log(x) log(x + 2) log(x + 1) log(x)
---------- + ---------- + ---------- >= ---------- + ---------- + ----------
log(x) log(x + 1) log(x + 2) log(x) log(x + 2) log(x + 1)
$$\left(\frac{\log{\left(x + 2 \right)}}{\log{\left(x + 1 \right)}} + \frac{\log{\left(x + 1 \right)}}{\log{\left(x \right)}}\right) + \frac{\log{\left(x \right)}}{\log{\left(x + 2 \right)}} \geq \left(\frac{\log{\left(x + 1 \right)}}{\log{\left(x + 2 \right)}} + \frac{\log{\left(x + 2 \right)}}{\log{\left(x \right)}}\right) + \frac{\log{\left(x \right)}}{\log{\left(x + 1 \right)}}$$