CAT 2018 Quant Questions

Question:
\({\log _{12}}81 = p,then\;3\left( {\frac{{4 - p}}{{4 + p}}} \right)\) is equal to

log416
log68
log616
log28
Show Answer
Correct Answer: 2

Given that: $\log_{12}{81}=p$

$\Rightarrow$ $\log_{81}{12}=\frac{1}{p}$

$\Rightarrow$ $4\log_{3}{3*4}=\frac{1}{p}$

$\Rightarrow$ $1+\log_{3}{4}=\frac{4}{p}$

Using Componendo and Dividendo,

$\Rightarrow$ $\frac{1+\log_{3}{4}-1}{1+\log_{3}{4}+1}=\frac{4-p}{4+p}$

$\Rightarrow$ $\frac{\log_{3}{4}}{2+\log_{3}{4}}=\frac{4-p}{4+p}$

$\Rightarrow$ $\frac{\log_{3}{4}}{\log_{3}{9}+\log_{3}{4}}=\frac{4-p}{4+p}$

$\Rightarrow$ $\frac{\log_{3}{4}}{\log_{3}{36}}=\frac{4-p}{4+p}$

$\Rightarrow$ $3*\frac{4-p}{4+p}=\frac{3\log_{3}{4}}{\log_{3}{36}}$

$\Rightarrow$ $3*\frac{4-p}{4+p}=\frac{\log_{3}{64}}{\log_{3}{36}}$

$\Rightarrow$ $3*\frac{4-p}{4+p}=\log_{36}{64}$

$\Rightarrow$ $3*\frac{4-p}{4+p}=\log_{6^2}{8^2}=\log_{6}{8}$.

Also Check: 841+ CAT Quant Questions with Solutions


CAT Quant Online Course


  • 1000+ Practice Problems
  • Detailed Theory of Every Topics
  • Online Live Sessions for Doubt Clearing
  • All Problems with Video Solutions
₹ 2999

CAT 2018 Questions Paper with Solution PDF Download


Back to Main Page


CAT 2018 Quant Questions
5 (100%) 10 votes