To convert a logarithmic equation to its exponential form, we need to use the fundamental relationship between logarithms and exponents.
Given the logarithmic equation:
[tex]\[ \log_m(y) = s \][/tex]
Here’s the step-by-step process to convert it into exponential form:
1. Understand the relationship: The logarithmic equation [tex]\(\log_m(y) = s\)[/tex] represents the power [tex]\(s\)[/tex] to which the base [tex]\(m\)[/tex] must be raised to obtain the value [tex]\(y\)[/tex].
2. Express in exponential form: By definition, [tex]\(\log_m(y) = s\)[/tex] means that:
[tex]\[ m^s = y \][/tex]
So, the equivalent exponential form of the logarithmic equation [tex]\(\log_m(y) = s\)[/tex] is:
[tex]\[ m^s = y \][/tex]
This means that if [tex]\(m\)[/tex] raised to the power of [tex]\(s\)[/tex] equals [tex]\(y\)[/tex], the logarithm base [tex]\(m\)[/tex] of [tex]\(y\)[/tex] is [tex]\(s\)[/tex]. Hence, the solution of the given logarithmic equation in exponential form is:
[tex]\[ m^s = y \][/tex]
