Question

If $2^{{\log }_{3}P}=5$, then $p^{{\log }_{5}4}$ equals

• A. 1
• B. 3
• C. 9
• D. 25

Answer 1

Answer: (C)

$2^{{\log }_{3}P}=5\Rightarrow {\log }_{3}p{\log }_{5}2=1\Rightarrow {\log }_{3}p={\log }_{2}5$
$\Rightarrow p=3^{{\log }_{2}5}$
$\Rightarrow (p{)}^{{\log }_{5}4}={\left(3^{{\log }_{2}5}\right)}^{{\log }_{5}4}=3^{{\log }_{2}5\cdot 2{\log }_{5}2}=3^2=9$