2a)
[tex]\rightarrow \sf 2^{x+1} = 2^x + 4[/tex]
[tex]\rightarrow \sf 2^{x+1} -2^x = 4[/tex]
[tex]\rightarrow \sf 2^1 * 2^x -2^x = 2^2[/tex]
[tex]\rightarrow \sf 2^x\left(2^1-1\right) = 2^2[/tex]
[tex]\rightarrow \sf 2^x\left(1) = 2^2[/tex]
[tex]\rightarrow \sf 2^x = 2^2[/tex]
[tex]\rightarrow \sf x= 2[/tex]
2b)
[tex]\rightarrow \sf 2^x + 2^{x - 2} = 5[/tex]
[tex]\rightarrow \sf 2^x + 2^{x} \div 2^2 = 5[/tex]
[tex]\rightarrow \sf 2^x + \dfrac{2^{x}}{2^2} = 5[/tex]
[tex]\rightarrow \sf 2^x(1 + \dfrac{1}{4} ) = 5[/tex]
[tex]\rightarrow \sf 2^x(1.25 ) = 5[/tex]
[tex]\rightarrow \sf 2^x = 5 \div 1.25[/tex]
[tex]\rightarrow \sf 2^x =4[/tex]
[tex]\rightarrow \sf 2^x =2^2[/tex]
[tex]\rightarrow \sf x=2[/tex]
