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If $\log (\text{P}) = (1/2)\log (\text{Q}) = (1/3)\log (\text{R})$, then which of the following options is TRUE?

1. $\text{P}^2 = \text{Q}^3\text{R}^2$
2. $\text{Q}^2=\text{P}\text{R}$
3. $\text{Q}^2 = \text{R}^3\text{P}$
4. $\text{R}=\text{P}^2\text{Q}^2$
edited | 1.2k views

$B$. is the answer.

Following logarithm formula, we get:
$P=Q^{\frac{1}{2}}=R^{\frac{1}{3}}$
So, $Q^{2}= P^{4}= P\times P^{3}=PR.$
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