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

Answer

Expert–verified

Hide Steps

Answer

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

Steps

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 $x = \boxed{\frac{3}{4}}$.