Certainly! Let's solve the given logarithmic equation step-by-step and rewrite it without logarithms.
The initial equation is:
[tex]\[
\log (x-8) - \log (x-2) = \log 3
\][/tex]
1. Apply the properties of logarithms: Recall that \(\log a - \log b = \log \left( \frac{a}{b} \right) \). Use this property to combine the logarithms on the left side.
[tex]\[
\log \left( \frac{x-8}{x-2} \right) = \log 3
\][/tex]
2. Exponentiate both sides to remove the logarithms: Since the logarithms are equal, their arguments must also be equal.
[tex]\[
\frac{x-8}{x-2} = 3
\][/tex]
Therefore, the equation rewritten without logarithms is:
[tex]\[
\frac{x-8}{x-2} = 3
\][/tex]
