Certainly! Let's solve the given equation step-by-step.
We are given:
[tex]\[
\log (x-14) - \log (x-6) = \log 3
\][/tex]
The properties of logarithms tell us that the difference of two logarithms can be expressed as the logarithm of a quotient. Therefore, we can rewrite the given equation as:
[tex]\[
\log \left( \frac{x-14}{x-6} \right) = \log 3
\][/tex]
If [tex]\(\log a = \log b\)[/tex], then it must be that [tex]\(a = b\)[/tex]. Thus, we can drop the logarithms and set the arguments equal to each other:
[tex]\[
\frac{x-14}{x-6} = 3
\][/tex]
So the equation without logarithms is:
[tex]\[
\frac{x-14}{x-6} = 3
\][/tex]
This is the exact form of the equation rewritten without logarithms.
