Question

Solve the following equation: 2^(x+2)=4^2
. What is the missing value?(1 point)

Answer 1

To solve the equation \( 2^{(x+2)} = 4^2 \), we can first express \( 4^2 \) in terms of base 2.

We know that:

\[
4 = 2^2
\]

Thus,

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

Now we can rewrite the original equation:

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

Since the bases are the same, we can set the exponents equal to each other:

\[
x + 2 = 4
\]

Now, we can solve for \( x \):

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

Therefore, the missing value is \( \boxed{2} \).