Apply logarithm properties.

Here are the solutions to the problems:

: Solve the equation $\log_4 x^2 - 6\log_4 4 - 1 = 0$.

Step 1: Apply logarithm properties.
We use the properties $\log_b a^c = c \log_b a$ and $\log_b b = 1$.

$$2\log_4 x - 6(1) - 1 = 0$$

Step 2: Simplify the equation.

$$2\log_4 x - 6 - 1 = 0$$ $$2\log_4 x - 7 = 0$$

Step 3: Isolate the logarithm term.

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