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Popular >

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

Notación decimal

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

Pasos de solución

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

Mover

2 lo g_{2} (x + 4)

al lado izquierdo

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

Mover

3 x

al lado derecho

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

Mover

1

al lado derecho

- 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 )}

Ejemplos populares

log_{10}(x-2)(3x^2-x-1)>0

lo g_{10} (x - 2) (3 x^{2} - x - 1) > 0

2-log_{10}(4x)>= 0

2 - lo g_{10} (4 x) \geq 0

log_{2}(x-1)>-1

lo g_{2} (x - 1) > - 1

log_{x-2}(3x^2-x-1)>0

lo g_{x - 2} (3 x^{2} - x - 1) > 0

log_{4}(x^2+2x)>log_{2}(x-4)

lo g_{4} (x^{2} + 2 x) > lo g_{2} (x - 4)