To solve for [tex]\( y \)[/tex] given the equation [tex]\( y = 2 \cdot 3^x \)[/tex] and [tex]\( x = 3 \)[/tex]:
1. Start by plugging in the value of [tex]\( x \)[/tex] into the equation:
[tex]\[
y = 2 \cdot 3^x
\][/tex]
When [tex]\( x = 3 \)[/tex]:
[tex]\[
y = 2 \cdot 3^3
\][/tex]
2. Next, calculate [tex]\( 3^3 \)[/tex]:
[tex]\[
3^3 = 3 \cdot 3 \cdot 3 = 27
\][/tex]
3. Now, substitute [tex]\( 3^3 \)[/tex] with 27 back into the equation:
[tex]\[
y = 2 \cdot 27
\][/tex]
4. Finally, perform the multiplication to find [tex]\( y \)[/tex]:
[tex]\[
y = 54
\][/tex]
So, the value of [tex]\( y \)[/tex] is [tex]\( 54 \)[/tex].
