Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Solve the equation. Give the solution in exact form.

[tex]\[ \log (x-8)-\log (x-2)=\log 3 \][/tex]

Rewrite the given equation without logarithms. Do not solve for \( x \).

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

Sagot :

GinnyAnswer
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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.