Problem
Solve the equation. \[ 4^{(12-3 x)}=64 \] A. [3] B. $\{16\}$ C. $\{-3\}$ D. $\{-16\}$
Solution
Step 1 ：Given the equation \(4^{(12-3x)}=64\).
Step 2 ：We know that 64 can be written as \(4^3\) and 4 can be written as \(2^2\).
Step 3 ：So, we can rewrite the equation as \((2^2)^{(12-3x)}=2^6\).
Step 4 ：Simplifying this gives \(2^{2(12-3x)}=2^6\).
Step 5 ：Since the bases are equal, the exponents must be equal. So, we have \(2(12-3x)=6\).
Step 6 ：Solving this equation will give us the value of x.
Step 7 ：Final Answer: The solution to the equation \(4^{(12-3 x)}=64\) is \(\boxed{3}\).
