Question

Melanie is solving a puzzle. Help her find the possible values of x and y which are true for the given expression.

$3^x$ = y

• A. x = 3, y = 9
• B. x = 4, y = 27
• C. x = 5, y = 81
• D. x = 6, y = 729

Answer 1

The correct option is D x = 6, y = 729

Consider x = 3, y = 9
The given expression is $3^x$ = y
Let us substitute x = 3, in $3^x$ = y
$⟹$ $3^3$ = 3 $\times$ 3 $\times$ 3 = 27
However, y is given as 9.
Hence, this does not satisfy the given expression.

Consider x = 4, y = 27
Let us substitute x = 4, in $3^x$ = y
$⟹$ $3^4$ = 3 $\times$ 3 $\times$ 3 $\times$ 3 = 81
However, y is given as 27.
Hence, this does not satisfy the given expression.

Consider x = 5, y = 81
Let us substitute x = 5, in $3^x$ = y
$⟹$ $3^5$ = 3 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 3 = 243
However, y is given as 81.
Hence, this does not satisfy the given expression.


Consider x = 6, y = 729
Let us substitute x = 6 in $3^x$ = y
$⟹$ $3^6$ = 3 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 3 = 729
Here, y is given as 729.
Hence, this satisfies the given expression.

Hence, the value of x and y are 6 and 729 in the given expression.