Question

solve 2^x-2+2^3-x=3

answer is x=2 or 3​

Answer 1

$HEYA \: \\ \\ 2 {}^{x} \times 2 {}^{ - 2} + 2 {}^{3} \times 2 {}^{ - x} = 3 \\ \\ put \: 2 {}^{x} = z \: \: so \: that \: 2 {}^{ - x} = 1 \div z \\ \\ (z \div 4) + (8 \div z) = 3 \\ \\ z {}^{2} + 32 - 12z = 0 \\ \\ z {}^{2} - 12z + 32 = 0 \\ \\ z {}^{2} - 8z - 4z + 32 = 0 \\ \\ z(z - 8) - 4(z - 8) = 0 \\ \\ (z - 4) = 0 \: \: \: or \: (z - 8) = 0 \\ \\ z = 8 \: \: or \: \: \: z = 4 \\ \\ 2 {}^{x} = 8 \: \: \: or \: \: \: 2 {}^{x} = 4 \\ \\ 2 {}^{x} = 2 {}^{3} \: \: \: or \: \: \: 2 {}^{x} = 2 {}^{2} \\ \\ compare \: powers \: of \: 2 \: we \: have \: \: \\ \\ x \: = 3 \: \: \: or \: \: \: x = 2$