Question

If $3^{{\left({\log }_{3}5\right)}^x}=5^{{\left({\log }_{5}3\right)}^2}$ then the value of $x$ is equal to

• A. -1
• B. 1
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

Answer: (A)

$\Theta 3^{{\left({\log }_{3}5\right)}^x}={\left(5^{{\log }_{5}3}\right)}^{{\log }_{5}3}$
$=3^{{\log }_{5}3}$
$\Rightarrow {\left({\log }_{3}5\right)}^x={\log }_{5}3=\frac{1}{{\log }_{3}5}$
$x=-1$