Let's consider the given logarithmic equation:
[tex]\[ \log_{14}(537824) = 5 \][/tex]
To convert a logarithmic equation to exponential form, remember that a logarithmic equation of the form:
[tex]\[ \log_b(a) = c \][/tex]
can be rewritten in exponential form as:
[tex]\[ b^c = a \][/tex]
Here, [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.
1. Identify the base ([tex]\(b\)[/tex]), result of the logarithm ([tex]\(c\)[/tex]), and the number being logged ([tex]\(a\)[/tex]).
- The base [tex]\(b\)[/tex] is [tex]\(14\)[/tex].
- The result of the logarithm [tex]\(c\)[/tex] is [tex]\(5\)[/tex].
- The number being logged [tex]\(a\)[/tex] is [tex]\(537824\)[/tex].
2. Substitute these values into the exponential form:
[tex]\[ b^c = a \][/tex]
3. Plug in [tex]\(b = 14\)[/tex], [tex]\(c = 5\)[/tex], and [tex]\(a = 537824\)[/tex]:
[tex]\[ 14^5 = 537824 \][/tex]
Therefore, the exponential form of [tex]\(\log_{14}(537824) = 5\)[/tex] is:
[tex]\[ 14^5 = 537824 \][/tex]
