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Popular Álgebra >

exln(x)=(ln(x))/(ex)

Solución

e x ln (x) = \frac{ln ( x )}{e x}

Solución

x = 1, x = \frac{1}{e}

+1

Decimal

x = 1, x = 0.36787 \dots

Pasos de solución

e x ln (x) = \frac{ln ( x )}{e x}

Multiplicar ambos lados por

e x

e x ln (x) e x = \frac{ln ( x )}{e x} e x

Simplificar

e x ln (x) e x : e^{2} x^{2} ln (x)

e^{2} x^{2} ln (x) = ln (x)

Desplace

ln (x)

a la izquierda

e^{2} x^{2} ln (x) - ln (x) = 0

Factorizar

e^{2} x^{2} ln (x) - ln (x) : ln (x) (e^{2} x^{2} - 1)

ln (x) (e^{2} x^{2} - 1) = 0

Usando la propiedad del factor cero:

Si

ab = 0

entonces

a = 0

o

b = 0

ln (x) = 0 or e^{2} x^{2} - 1 = 0

Resolver

ln (x) = 0 : x = 1

Resolver

e^{2} x^{2} - 1 = 0 : x = \frac{1}{e}, x = - \frac{1}{e}

Verificar las soluciones:

x = 1

Verdadero

, x = \frac{1}{e}

Verdadero

, x = - \frac{1}{e}

Falso

Las soluciones son

x = 1, x = \frac{1}{e}

Gráfica

Ejemplos populares

solvefor x,ln(y)+ln(x)=c

so l v e f or x, ln (y) + ln (x) = c

log_{5}(6x)+5=3

lo g_{5} (6 x) + 5 = 3

log_{4}(x+3)-log_{4}(x-5)=2

lo g_{4} (x + 3) - lo g_{4} (x - 5) = 2

4log_{10}(2n)-7=-11

4 lo g_{10} (2 n) - 7 = - 11

log_{10}(x)=5-x

lo g_{10} (x) = 5 - x