Question

If ${\left(36\right)}^x={\left(216\right)}^y$ , then what is the ratio of x : y ?

• A. 2:3
• B. 1:6
• C. 3:2
• D. 6:1

Answer 1

The correct option is C 3:2

${\left(36\right)}^x$ can be written as ${\left(6^2\right)}^x$
Therefore, ${\left(36\right)}^x=6^{2x}$
Similarly, ${\left(216\right)}^y={\left(6^3\right)}^y=6^{3y}$
Therefore , $6^{2x}=6^{3y}$

We can say that 2x = 3y

$\frac{x}{y}=\frac{3}{2}$

Ratio of x:y = 3:2
So, option c is correct.