If $\log _{4} x=3$, find the value of $x$ without a calculator. \[ \mathrm{x}= \] (Simplify your answer.)

Step 1 ：The question is asking for the value of x given that \(\log _{4} x=3\). This is a logarithmic equation. The base of the logarithm is 4 and the result is 3.

Step 2 ：To solve for x, we need to convert the logarithmic equation to an exponential equation. The base of the logarithm becomes the base of the power, the result of the logarithm becomes the exponent, and x is the result of the power.

Step 3 ：base = 4, exponent = 3, so x = \(4^3\)

Step 4 ：Simplify \(4^3\) to get x = 64

Step 5 ：Final Answer: The value of x is \(\boxed{64}\)