Question

solve the equation for r.
\\(\log_{r} 3 = \frac{1}{3}\\)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. \\(r = \square\\) (simplify your answer.)
\\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Convert log to exponential form

Recall that if $\log_{a}b = c$, then $a^{c}=b$. So for $\log_{r}3=\frac{1}{3}$, we get $r^{\frac{1}{3}} = 3$.

Step2: Solve for r

To solve for $r$, we cube both sides of the equation. Cubing the left side: $(r^{\frac{1}{3}})^{3}=r^{\frac{1}{3}\times3}=r$. Cubing the right side: $3^{3}=27$. So $r = 27$.

Answer:

A. $r = 27$