To rewrite the logarithmic equation [tex]\(\log_7 343 = 3\)[/tex] in exponential form, we need to understand the relationship between logarithms and exponents.
The logarithmic equation [tex]\(\log_b A = C\)[/tex] is equivalent to the exponential equation [tex]\(b^C = A\)[/tex], where:
- [tex]\(b\)[/tex] is the base of the logarithm,
- [tex]\(A\)[/tex] is the number we are taking the logarithm of,
- and [tex]\(C\)[/tex] is the result of the logarithm.
Given the logarithmic equation [tex]\(\log_7 343 = 3\)[/tex]:
- The base [tex]\(b\)[/tex] is [tex]\(7\)[/tex],
- The number [tex]\(A\)[/tex] is [tex]\(343\)[/tex],
- and the result [tex]\(C\)[/tex] is [tex]\(3\)[/tex].
Rewriting this logarithmic equation in exponential form:
- The base [tex]\(7\)[/tex] raised to the power of [tex]\(3\)[/tex] gives the number [tex]\(343\)[/tex].
Therefore, the exponential form is:
[tex]\[ 7^3 = 343 \][/tex]
So, the correct answer is:
B. [tex]\(7^3 = 343\)[/tex]
