20 votes 20 votes If $\log (\text{P}) = (1/2)\log (\text{Q}) = (1/3)\log (\text{R})$, then which of the following options is TRUE? $\text{P}^2 = \text{Q}^3\text{R}^2$ $\text{Q}^2=\text{P}\text{R}$ $\text{Q}^2 = \text{R}^3\text{P}$ $\text{R}=\text{P}^2\text{Q}^2$ Quantitative Aptitude gatecse-2011 quantitative-aptitude normal numerical-computation logarithms + – go_editor asked Sep 29, 2014 • edited Jul 30, 2015 go_editor 5.3k views answer comment Share Follow See 1 comment See all 1 1 comment reply Punit Sharma commented Jan 15, 2020 reply Follow Share Put P=$2^{10}$ Q=$2^{20}$ R= $2^{30}$ Put in options only b) option satisfies! 1 votes 1 votes Please log in or register to add a comment.
Best answer 32 votes 32 votes $B$. is the answer. Following logarithm formula, we get: $P=Q^{\frac{1}{2}}=R^{\frac{1}{3}}$ So, $Q^{2}= P^{4}= P\times P^{3}=PR.$ shree answered Oct 22, 2014 • edited Jun 8, 2018 by Milicevic3306 shree comment Share Follow See 1 comment See all 1 1 comment reply sidlewis commented Nov 21, 2018 reply Follow Share Simplest Approach! 5 votes 5 votes Please log in or register to add a comment.
4 votes 4 votes $log(P)=\frac{1}{2}log(Q)=\frac{1}{3}log(R)$ $=>P=Q^{\frac{1}{2}}=R^{\frac{1}{3}}$ 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 JashanArora answered Nov 27, 2019 JashanArora comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Answer is Option B. Ray Tomlinson answered Sep 14, 2023 Ray Tomlinson comment Share Follow See all 0 reply Please log in or register to add a comment.