Solve for $x$ \[ 2^{4 x}=8 \]

Step 1 ：The given equation is \(2^{4x} = 8\).

Step 2 ：We can express 8 as \(2^3\).

Step 3 ：So, the equation becomes \(2^{4x} = 2^3\).

Step 4 ：Since the bases are equal, the exponents must also be equal. Therefore, \(4x = 3\).

Step 5 ：Solving for x, we get \(x = \frac{3}{4}\).

Step 6 ：Final Answer: The solution to the equation \(2^{4x} = 8\) is \(x = \boxed{\frac{3}{4}}\).