Answered

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Solve the equation. Give the solution in exact form.

[tex]\[
\log (x-14) - \log (x-6) = \log 3
\][/tex]

Rewrite the given equation without logarithms. Do not solve for [tex]\(x\)[/tex].

[tex]\[\square\][/tex]

Sagot :

GinnyAnswer
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.
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