Solve the equation.
\[
4^{(12-3 x)}=64
\]
A. [3]
B. $\{16\}$
C. $\{-3\}$
D. $\{-16\}$

Answer

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Answer

Final Answer: The solution to the equation $4^{(12-3 x)}=64$ is $\boxed{3}$.

Steps

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 $\boxed{3}$.