Solve for $x$ \[ \log _{x} 49=2 \] Simplify your answer as much as possible.

Step 1 ：The given equation is in the form of a logarithm. The base of the logarithm is \(x\), the argument is \(49\), and the value 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 exponent will be \(x\), the exponent will be \(2\), and the result will be \(49\). This gives us the equation \(x^2 = 49\).

Step 3 ：We can then solve this equation for \(x\). The solutions to the equation are \(x = 7\) and \(x = -7\).

Step 4 ：However, in the context of logarithms, the base of a logarithm is always positive. Therefore, the only valid solution is \(x = 7\).

Step 5 ：Final Answer: \(\boxed{7}\)