Write the given exponential equation in logarithmic form.
\[
a^{2}+4=11
\]
The logarithmic form is

Step 1 ：Given the exponential equation \(a^{2}+4=11\).

Step 2 ：Subtract 4 from both sides of the equation to isolate the exponential part, resulting in \(a^{2} = 7\).

Step 3 ：Convert this to logarithmic form. The base of the logarithm will be the base of the exponent (which is 'a' in this case), the argument of the logarithm will be the result of the exponentiation (which is 7), and the result of the logarithm will be the exponent itself (which is 2).

Step 4 ：Solve for 'a' in the equation \(a^{2} = 7\), which gives two solutions: \(a = -\sqrt{7}\) and \(a = \sqrt{7}\).

Step 5 ：In the context of logarithms, we only consider the positive solution because the base of a logarithm is always positive. Therefore, we have \(a = \sqrt{7}\).

Step 6 ：Substitute \(a = \sqrt{7}\) into the logarithmic form of the equation, resulting in \(\log_{\sqrt{7}}7 = 2\).

Step 7 ：\(\boxed{\log_{\sqrt{7}}7 = 2}\) is the logarithmic form of the given equation.