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Popular Álgebra >

3x+1<2*log_{2}(x+4)

Solución

3 x + 1 < 2 \cdot lo g_{2} (x + 4)

Solución

- 4 < x < \frac{- 2 W _{0} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )} or x > \frac{- 2 W _{- 1} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )}

+2

Notación de intervalos

- 4, \frac{- 2 W _{0} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )} \cup \frac{- 2 W _{- 1} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )}, \infty

Decimal

- 4 < x < - 3.97737 \dots or x > 1.26413 \dots

Pasos de solución

3 x + 1 < 2 lo g_{2} (x + 4)

Desplace

2 lo g_{2} (x + 4)

a la izquierda

3 x + 1 - 2 lo g_{2} (x + 4) < 0

Desplace

3 x

a la derecha

1 - 2 lo g_{2} (x + 4) < - 3 x

Desplace

1

a la derecha

- 2 lo g_{2} (x + 4) < - 3 x - 1

Multiplicar ambos lados por

- 1

2 lo g_{2} (x + 4) > 3 x + 1

Dividir ambos lados entre

2

lo g_{2} (x + 4) > \frac{3 x + 1}{2}

Para a>1, si

f (x) > g (x),

entonces

a^{f (x)} > a^{g (x)}

a = 2

2^{l o g_{2} (x + 4)} > 2^{\frac{3 x + 1}{2}}

Simplificar

2^{l o g_{2} (x + 4)} : x + 4

x + 4 > 2^{\frac{3 x + 1}{2}}

Resolver

x + 4 > 2^{\frac{3 x + 1}{2}} : x < \frac{- 2 W _{0} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )} or x > \frac{- 2 W _{- 1} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )}

Encontrar valores positivos para los logaritmos:

x > - 4

Combinar los rangos

x < \frac{- 2 W _{0} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )} or x > \frac{- 2 W _{- 1} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )} and x > - 4

Mezclar intervalos sobrepuestos

- 4 < x < \frac{- 2 W _{0} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )} or x > \frac{- 2 W _{- 1} ( - \frac{3 l n ( 2 )}{2 e ^{\frac{11 l n ( 2 )}{2}}} ) - 12 ln ( 2 )}{3 ln ( 2 )}

Gráfica

Ejemplos populares

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