To solve the given problem, we start by analyzing the equation [tex]\(2^x = 16\)[/tex].
Step 1: Express 16 as a power of 2.
We know that:
[tex]\[ 16 = 2^4 \][/tex]
So, we can write:
[tex]\[ 2^x = 2^4 \][/tex]
Step 2: Since the bases are the same on both sides of the equation, we can equate the exponents:
[tex]\[ x = 4 \][/tex]
Step 3: Now, we need to find the value of [tex]\(3^x\)[/tex] using the value of [tex]\(x\)[/tex] we just found:
[tex]\[ x = 4 \][/tex]
Thus:
[tex]\[ 3^x = 3^4 \][/tex]
Step 4: Calculate [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Therefore, [tex]\(3^x = 81\)[/tex], and the correct answer is:
[tex]\[ \boxed{81} \][/tex]
So the answer is:
D 81
