To determine the value of [tex]\(x\)[/tex] given the logarithmic expression [tex]\(\log_3 x = 4\)[/tex], we need to convert the logarithmic equation into its exponential form.
Given:
[tex]\[
\log_3 x = 4
\][/tex]
The logarithmic form [tex]\(\log_3 x = 4\)[/tex] translates to the exponential form:
[tex]\[
3^4 = x
\][/tex]
Now we calculate [tex]\(3^4\)[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3
\][/tex]
Breaking it down:
[tex]\[
3 \times 3 = 9
\][/tex]
[tex]\[
9 \times 3 = 27
\][/tex]
[tex]\[
27 \times 3 = 81
\][/tex]
Thus, [tex]\(3^4 = 81\)[/tex].
So, the value of [tex]\(x\)[/tex] is:
[tex]\[
x = 81
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{81}
\][/tex]
So the answer is B. 81.
