[tex]2^\text{x}+2^{\text{x}+2} = 16 \\ \\ 2^\text{x}+2^\text{x}\cdot2^2 = 16 \\ \\2^\text{x} +2^\text{x}\cdot 4 = 16 \\ \\ 2^\text{x}\cdot (1+4) = 16 \\ \\ 2^\text{x}\cdot 5 = 16\\ \\ 2^\text{x} = \dfrac{16}{5} \\ \\ \text{x} = \log_{\big2}\dfrac{16}{5}\\ \\ \text{x} = \log_{\big2}16 - \log_{\big2}5 \\ \\ \text{x} = 4-\log_{\big2}5[/tex]
