Question

${2}^{x - 1} + 5 \times {2}^{x} = 11$

Answer 1

$2^{x-1}+5.2^x=11\\ 2^x.2^{-1}+5.2^x=11\\ 2^x.\frac{1}{2}+5.2^x=11\\\\ \frac{2^x}{2}+5.2^x=11\\\\ \frac{2^x+2.5.2^x=2.11}{2}\\\\ 2^x+10.2^x=22\\ 11.2^x=22\\ 2^x=\frac{22}{11}\\\\ 2^x=2\\ 2^x=2^1\\ x=1$