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Popular >

2.5x^2=5xlog_{2}(x)4

Solución

2.5 x^{2} = 5 x lo g_{2} (x) 4

Solución

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

+1

Notación decimal

x = 43.55926 \dots, x = 1.09999 \dots

Pasos de solución

2.5 x^{2} = 5 x lo g_{2} (x) \cdot 4

Intercambiar lados

5 x lo g_{2} (x) \cdot 4 = 2.5 x^{2}

Multiplicar ambos lados por

10

200 x lo g_{2} (x) = 25 x^{2}

Mover

25 x^{2}

al lado izquierdo

200 x lo g_{2} (x) - 25 x^{2} = 0

Factorizar

200 x lo g_{2} (x) - 25 x^{2} : 25 x (8 lo g_{2} (x) - x)

25 x (8 lo g_{2} (x) - x) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

x = 0 or 8 lo g_{2} (x) - x = 0

Resolver

8 lo g_{2} (x) - x = 0 : x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Verificar las soluciones:

x = 0

Falso

, x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Verdadero

, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Verdadero

Las soluciones son

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Ejemplos populares

log_{3}(x^2-x-4)=2

lo g_{3} (x^{2} - x - 4) = 2

log_{4}(x)-4log_{x}(4)+3=0

lo g_{4} (x) - 4 lo g_{x} (4) + 3 = 0

0.54 = ln (y)

ln (4 x) = 2.0706

lo g_{10} (h) = 1