What is the value of $x$ in the equation $\log _{7}(x)=2 ?$

Step 1 ：The question is asking for the value of \(x\) that satisfies the equation \(\log _{7}(x)=2\). This is a logarithmic equation. The base of the logarithm is 7 and the result of the logarithm is 2.

Step 2 ：To solve for \(x\), we can convert the logarithmic equation to an exponential equation. The base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and \(x\) is the result of the exponentiation.

Step 3 ：So, the equation \(\log _{7}(x)=2\) is equivalent to the equation \(7^2 = x\).

Step 4 ：Calculating \(7^2\) gives us \(x = 49\).

Step 5 ：Final Answer: The value of \(x\) that satisfies the equation \(\log _{7}(x)=2\) is \(\boxed{49}\).