Question

solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer. \\(\log_{3}(x + 3) = 2\\)\
rewrite the given equation without logarithms. do not solve for x.

Explanation:

Step1: Recall the logarithmic definition

The logarithmic equation \(\log_{b}a = c\) can be rewritten in exponential form as \(b^{c}=a\), where \(b>0\), \(b
eq1\), and \(a > 0\).

Step2: Apply the definition to the given equation

For the equation \(\log_{3}(x + 3)=2\), here \(b = 3\), \(c=2\), and \(a=x + 3\). Using the exponential form conversion, we get \(3^{2}=x + 3\).

Answer:

\(3^{2}=x + 3\) (or simplified as \(9=x + 3\) but since the problem says to rewrite without logarithms and not solve, \(3^{2}=x + 3\) is the rewritten form)