If $\log (\text{P}) = (1/2)\log (\text{Q}) = (1/3)\log (\text{R})$, then which of the following options is TRUE?
Simplest Approach!
$log(P)=\frac{1}{2}log(Q)=\frac{1}{3}log(R)$
$=>P=Q^{\frac{1}{2}}=R^{\frac{1}{3}}$
Now
$Q^{2}=Q^{\frac{1}{2}}Q^{\frac{1}{2}}Q^{\frac{1}{2}}Q^{\frac{1}{2}}$
$=>Q^{2}=PR^{\frac{1}{3}}R^{\frac{1}{3}}R^{\frac{1}{3}}$
$=>Q^{2}=PR$
Option B