Question

Necesito resolver este ejercicio LOG2(2×+6)=3

Answer 1

$\log _{10}\left(2\right)\left(2x+6\right)=3\quad :\quad x=\frac{3-6\log _{10}\left(2\right)}{2\log _{10}\left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=1.98289\dots \right)$

Pasos

$\log _{10}\left(2\right)\left(2x+6\right)=3$

$\mathrm{Dividir\:ambos\:lados\:entre\:}\log _{10}\left(2\right)$

$\frac{\log _{10}\left(2\right)\left(2x+6\right)}{\log _{10}\left(2\right)}=\frac{3}{\log _{10}\left(2\right)}$

$Simplificar$

$2x+6=\frac{3}{\log _{10}\left(2\right)}$

$\mathrm{Restar\:}6\mathrm{\:de\:ambos\:lados}$

$2x+6-6=\frac{3}{\log _{10}\left(2\right)}-6$

$Simplificar$

$2x+6=\frac{3}{\log _{10}\left(2\right)}$

$\mathrm{Dividir\:ambos\:lados\:entre\:}2$

$\frac{2x}{2}=\frac{\frac{3}{\log _{10}\left(2\right)}}{2}-\frac{6}{2}$

$\mathrm{Simplificar}$

$x=\frac{3-6\log _{10}\left(2\right)}{2\log _{10}\left(2\right)}$

Answer 2

Respuesta:

x=1

Explicación paso a paso:

Log2(2x+6)=3

Determina el rango definido

Log2(2x+6)=3>-3

Factorizar la expresión

Log2(2x+3))=3

Expandir la expresión

Log2(2)+log2(x+3)=3

Evalúar el logaritmo

1+log2(x+3)=3

Log2(x+3)=3-1

Log2(x+3)=2

x+3=2²

x+3=4

x=4-3

x=1