QuestionSolve for $r$ : $$\begin{array}{l} \log _{3}(r+3)=-1 \\ r=\square \end{array}$$

Studdy Solution
Calculate $3^{-1}$ and solve for $r$:
$$3^{-1} = \frac{1}{3}$$
So, the equation becomes:
$$\frac{1}{3} = r + 3$$
Subtract 3 from both sides to solve for $r$:
$$r = \frac{1}{3} - 3$$
Convert 3 to a fraction with a denominator of 3:
$$r = \frac{1}{3} - \frac{9}{3}$$
$$r = \frac{1 - 9}{3}$$
$$r = \frac{-8}{3}$$
The value of $r$ is:
$$\boxed{-\frac{8}{3}}$$