To rewrite the logarithmic equation [tex]\(\log_7 343 = 3\)[/tex] in exponential form, we start with the basic property of logarithms. The logarithmic equation [tex]\(\log_b a = c\)[/tex] can be rewritten as [tex]\(b^c = a\)[/tex]. Here, [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(a\)[/tex] is the number, and [tex]\(c\)[/tex] is the logarithm value.
Given [tex]\(\log_7 343 = 3\)[/tex], we identify:
- [tex]\(b = 7\)[/tex]
- [tex]\(a = 343\)[/tex]
- [tex]\(c = 3\)[/tex]
Using the property of logarithms:
[tex]\[
\log_b a = c \quad \text{is equivalent to} \quad b^c = a
\][/tex]
Substitute the identified values:
[tex]\[
7^3 = 343
\][/tex]
So, the equation [tex]\(\log_7 343 = 3\)[/tex] rewritten in exponential form is:
[tex]\[
7^3 = 343
\][/tex]
Therefore, the correct answer is:
B. [tex]\(7^3 = 343\)[/tex]
