solve the follwing equation 2^(x+2) = 4^2

Answer 1

To solve the equation \( 2^{(x+2)} = 4^2 \), we first recognize that \( 4 \) can be expressed as \( 2^2 \). Therefore, we can write \( 4^2 \) as follows:

\[ 4^2 = (2^2)^2 = 2^{2 \cdot 2} = 2^4 \]

Now we can rewrite the original equation:

\[ 2^{(x+2)} = 2^4 \]

Since the bases are the same, we can equate the exponents:

\[ x + 2 = 4 \]

Now, we solve for \( x \):

\[ x = 4 - 2 \] \[ x = 2 \]

Thus, the solution to the equation \( 2^{(x+2)} = 4^2 \) is

\[ \boxed{2} \]

Answer 2

what is the missing value

Answer 3

It looks like there may have been a miscommunication regarding what you're looking for with "the missing value." If you are referring to the solution found in the previous equation, the missing value (solution for \( x \) in the equation \( 2^{(x+2)} = 4^2 \)) is \( x = 2 \).

If you meant something else or have a different context or a specific equation where a value is missing, please provide more details so I can assist you further!