Question

resuelve
${2}^{x} . {4}^{x + 1} . {8}^{x + 2} = {16}^{x + 3} \: \: hallar \: m = 7 x + 3$
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Answer 1

${2}^{x} . {4}^{x + 1} . {8}^{x + 2} = 16 {x}^{x + 3} \\ {2}^{x} . {( {2}^{2} )}^{x + 1} . {( {2}^{3} )}^{x + 2} = {( {2}^{4} )}^{x + 3} \\ {2}^{x} . {2}^{(2x + 2)} . {2}^{(3x + 6)} = {2}^{(4x + 12)} \\ {2}^{(x + 2x + 2 + 3x + 6)} = {2}^{(4x + 12)} \\ {2}^{(6x + 8)} = {2}^{(4x + 12)}$

Entonces :

$6x + 8 = 4x + 12 \\ 2x = 4 \\ x = 2$

Como :

m = 7x + 3

m = 7(2)+3

m = 14 + 3

m = 17

Saludos.