Solve for $x$ in each equation below. It may be helpful to convert the equation into exponential form.
(A) $\log _{a} a=x$
\[
x=
\]
(B) $\log _{a} a^{6}=x$
\[
x=
\]
(C) $\log _{a} a^{2}=x$
\[
x=\square
\]
(D) $\log _{a} a^{n}=x$
\[
x=
\]
Answer
Final Answer: \(\boxed{x=1}\) for (A), \(\boxed{x=6}\) for (B), \(\boxed{x=2}\) for (C), \(\boxed{x=n}\) for (D)
Step 1 ：Convert the equation into exponential form.
Step 2 ：The logarithm base \(a\) of \(a\) to the power of \(n\) is \(n\).
Step 3 ：This is because the logarithm base \(a\) of \(b\) is the exponent to which \(a\) must be raised to get \(b\).
Step 4 ：So, in each of these equations, \(x\) is equal to the exponent of \(a\) in the argument of the logarithm.
Step 5 ：Final Answer: \(\boxed{x=1}\) for (A), \(\boxed{x=6}\) for (B), \(\boxed{x=2}\) for (C), \(\boxed{x=n}\) for (D)
