What integer $x$ satisfies the equation: $2^{x + 2} = 32$ ?
I notice that 32 is also a power of 2, namely $2^5$. So I can rewrite the equation as $2^{x + 2} = 2^5$. Now I can use the property that if the bases are equal, then the exponents must be equal as well. So I get $x + 2 = 5$. Subtracting 2 from both sides, I get $x = 3$. 