To solve this problem, we need to evaluate the function [tex]\( f(x) = 3^x \)[/tex] at [tex]\( x = 4 \)[/tex].
Let's break it down step by step:
1. Understand the function: We are given a function [tex]\( f(x) = 3^x \)[/tex]. This is an exponential function, where the base is 3 and the exponent is [tex]\( x \)[/tex].
2. Substitute [tex]\( x \)[/tex] with 4: To evaluate the function at [tex]\( x = 4 \)[/tex], we substitute 4 in place of [tex]\( x \)[/tex]:
[tex]\[
f(4) = 3^4
\][/tex]
3. Compute the exponentiation: We need to calculate [tex]\( 3 \)[/tex] raised to the power of [tex]\( 4 \)[/tex]:
[tex]\[
3^4
\][/tex]
4. Result: [tex]\( 3^4 \)[/tex] equals 81.
Thus, when the function [tex]\( f(x) = 3^x \)[/tex] is evaluated for [tex]\( x = 4 \)[/tex], the output is:
[tex]\(
81.
\)[/tex]
