Write the equation in exponential form: $\log _{49} 7=\frac{1}{2}$

Step 1 ：Write the equation in exponential form: $\log _{49} 7=\frac{1}{2}$

Step 2 ：The general form of a logarithmic equation is $\log_b a = c$, which can be converted into exponential form as $b^c = a$. Here, $b = 49$, $a = 7$, and $c = \frac{1}{2}$.

Step 3 ：The exponential form of the given logarithmic equation is $\boxed{49^{\frac{1}{2}} = 7}$