Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} \times 3^x \)[/tex], follow these steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
Start by replacing [tex]\( x \)[/tex] with [tex]\( 5 \)[/tex] in the expression for [tex]\( f(x) \)[/tex].
[tex]\[
f(5) = \frac{1}{9} \times 3^5
\][/tex]
2. Calculate [tex]\( 3^5 \)[/tex]:
Multiply 3 by itself five times:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply [tex]\( 243 \)[/tex] by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243
\][/tex]
4. Simplify the calculation:
[tex]\( \frac{1}{9} \times 243 \)[/tex] simplifies to dividing 243 by 9:
[tex]\[
f(5) = 27
\][/tex]
Therefore, the value of [tex]\( f(5) \)[/tex] is [tex]\(\boxed{27}\)[/tex].
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
Start by replacing [tex]\( x \)[/tex] with [tex]\( 5 \)[/tex] in the expression for [tex]\( f(x) \)[/tex].
[tex]\[
f(5) = \frac{1}{9} \times 3^5
\][/tex]
2. Calculate [tex]\( 3^5 \)[/tex]:
Multiply 3 by itself five times:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply [tex]\( 243 \)[/tex] by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243
\][/tex]
4. Simplify the calculation:
[tex]\( \frac{1}{9} \times 243 \)[/tex] simplifies to dividing 243 by 9:
[tex]\[
f(5) = 27
\][/tex]
Therefore, the value of [tex]\( f(5) \)[/tex] is [tex]\(\boxed{27}\)[/tex].
