QuestionJuly 18, 2025

Solve the equation. Give the solution in exact form. log_(3)(x+12)+log_(3)(x-12)=4 Rewrite the given equation without logarithms. Do not solve for x. (x+12)(x-12)=81 Select the correct choice below and, if necessary.fill in the answer box to complete your choice. A. The solution set is square (Type an exact solution using radicals as needed Use a comma to separate answers as needed.) B. The solution is the empty set.

Solve the equation. Give the solution in exact form. log_(3)(x+12)+log_(3)(x-12)=4 Rewrite the given equation without logarithms. Do not solve for x. (x+12)(x-12)=81 Select the correct choice below and, if necessary.fill in the answer box to complete your choice. A. The solution set is square (Type an exact solution using radicals as needed Use a comma to separate answers as needed.) B. The solution is the empty set.
Solve the equation. Give the solution in exact form.
log_(3)(x+12)+log_(3)(x-12)=4
Rewrite the given equation without logarithms. Do not solve for x.
(x+12)(x-12)=81
Select the correct choice below and, if necessary.fill in the answer box to complete your choice.
A. The solution set is  square 
(Type an exact solution using radicals as needed Use a comma to separate answers as needed.)
B. The solution is the empty set.

Solution
4.3(255 votes)

Answer

A. The solution set is 0, 24. Explanation 1. Combine Logarithms Use the property \log_b(m) + \log_b(n) = \log_b(mn) to combine: log_{3}((x+12)(x-12))=4. 2. Rewrite Equation Without Logarithms Convert logarithmic equation to exponential form: (x+12)(x-12)=3^4. 3. Simplify Exponential Expression Calculate 3^4: (x+12)(x-12)=81.

Explanation

1. Combine Logarithms<br /> Use the property $\log_b(m) + \log_b(n) = \log_b(mn)$ to combine: $log_{3}((x+12)(x-12))=4$.<br />2. Rewrite Equation Without Logarithms<br /> Convert logarithmic equation to exponential form: $(x+12)(x-12)=3^4$.<br />3. Simplify Exponential Expression<br /> Calculate $3^4$: $(x+12)(x-12)=81$.
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