Answered

What is this equation rewritten in exponential form?

[tex]\log _7 343=3[/tex]

A. [tex]3^7=343[/tex]

B. [tex]7^3=343[/tex]

C. [tex]343^x=7[/tex]

D. [tex]343^x=3[/tex]



Answer :

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]