Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex], follow these steps:
1. Substitute 5 for [tex]\( x \)[/tex] in the function.
Start with the expression:
[tex]\[
f(x) = \frac{1}{9}(3)^x
\][/tex]
When [tex]\( x = 5 \)[/tex], it becomes:
[tex]\[
f(5) = \frac{1}{9}(3)^5
\][/tex]
2. Evaluate [tex]\( (3)^5 \)[/tex].
Calculate [tex]\( 3 \)[/tex] raised to the power of 5:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
3. Multiply the result by [tex]\(\frac{1}{9}\)[/tex].
Now substitute [tex]\( 3^5 = 243 \)[/tex] back into the expression:
[tex]\[
f(5) = \frac{1}{9} \times 243
\][/tex]
Perform the multiplication:
[tex]\[
f(5) = \frac{243}{9} = 27
\][/tex]
Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\(\boxed{27}\)[/tex].
1. Substitute 5 for [tex]\( x \)[/tex] in the function.
Start with the expression:
[tex]\[
f(x) = \frac{1}{9}(3)^x
\][/tex]
When [tex]\( x = 5 \)[/tex], it becomes:
[tex]\[
f(5) = \frac{1}{9}(3)^5
\][/tex]
2. Evaluate [tex]\( (3)^5 \)[/tex].
Calculate [tex]\( 3 \)[/tex] raised to the power of 5:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
3. Multiply the result by [tex]\(\frac{1}{9}\)[/tex].
Now substitute [tex]\( 3^5 = 243 \)[/tex] back into the expression:
[tex]\[
f(5) = \frac{1}{9} \times 243
\][/tex]
Perform the multiplication:
[tex]\[
f(5) = \frac{243}{9} = 27
\][/tex]
Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\(\boxed{27}\)[/tex].
