To write the equation [tex]\(\log(t) = m\)[/tex] in exponential form, let's follow these steps:
1. Understand the logarithmic form: The given equation is [tex]\(\log(t) = m\)[/tex], where the base of the logarithm is implicitly 10, as it is a common logarithm.
2. Recall the definition of logarithms: The logarithmic statement [tex]\(\log_b(a) = c\)[/tex] implies that [tex]\(a = b^c\)[/tex], where:
- [tex]\(b\)[/tex] is the base,
- [tex]\(a\)[/tex] is the argument of the logarithm,
- [tex]\(c\)[/tex] is the exponent.
3. Apply the definition to our equation: Here, our logarithmic equation is [tex]\(\log_{10}(t) = m\)[/tex]. By the logarithmic definition, this means that:
[tex]\[
t = 10^m
\][/tex]
Thus, the exponential form of the equation [tex]\(\log(t) = m\)[/tex] is:
[tex]\[
t = 10^m
\][/tex]
This completes the conversion from logarithmic form to exponential form.
