Sure! To transform the given logarithmic equation [tex]\( \log(q) = t \)[/tex] into its exponential form, you can follow these steps:
1. Identify the base of the logarithm:
In this equation, [tex]\(\log(q)\)[/tex] is given without specifying its base. By convention, when the base is not specified, it is assumed to be the natural logarithm, which has a base of [tex]\(e\)[/tex].
2. Rewrite the logarithmic equation in terms of its exponential form:
The natural logarithm [tex]\(\log(q)\)[/tex] with base [tex]\(e\)[/tex] can be written as [tex]\(\ln(q)\)[/tex], where [tex]\( \ln(q) = t \)[/tex].
The general form of a logarithmic equation [tex]\(\log_b(x) = y\)[/tex] can be rewritten in its exponential form as [tex]\( x = b^y \)[/tex].
3. Apply the exponential operation:
Based on the above form, the equation [tex]\(\ln(q) = t\)[/tex] can be rewritten in its exponential form. Since [tex]\(\ln(q)\)[/tex] uses base [tex]\(e\)[/tex], this translates to:
[tex]\[
q = e^t
\][/tex]
So, the exponential form of the equation [tex]\(\log(q) = t\)[/tex] is:
[tex]\[
q = e^t
\][/tex]
