Answer :
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.
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.
