I interpret this as 2^(2x+3)=5*2^(x+1).
Take logs of each side: (2x+3)log2=log5 + (x+1)log2.
2xlog2+3log2=log5+xlog2+log2.
xlog2=log(5*2/8)=log1.25; x=log1.25/log2=0.32193 approx.
CHECK: Put this value into the original equation: 2^(2x+3)=12.5; 2^(x+1)=2.5 so 5*2.5=12.5. The equation balances.