Solve for $\mathrm{x}$ : \[ \begin{array}{l} \log _{x}\left(\frac{1}{4}\right)=-1 \\ x= \end{array} \]

Step 1 ：The given equation is in the form of a logarithm, where the base of the logarithm is x, the argument is 1/4, and the value of the logarithm is -1.

Step 2 ：We can convert this logarithmic equation into an exponential equation to solve for x. The base of the exponent will be x, the exponent will be -1, and the result will be 1/4.

Step 3 ：By solving the exponential equation, we find that the solution to the equation is x = 4. This means that if we substitute x = 4 into the original logarithmic equation, the equation holds true.

Step 4 ：Final Answer: The solution to the equation is \(\boxed{4}\).