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Popular >

solvefor x,f=e^{sin(x^2)}

Solución

resolver para

x, f = e^{s i n (x^{2})}

Solución

x = arcsin (ln (f)) + 2 πn, x = - arcsin (ln (f)) + 2 πn, x = π + arcsin (- ln (f)) + 2 πn, x = - π + arcsin (- ln (f)) + 2 πn

Pasos de solución

f = e^{s i n (x^{2})}

Intercambiar lados

e^{s i n (x^{2})} = f

Aplicar las leyes de los exponentes

e^{s i n (x^{2})} = f

Si

f (x) = g (x)

, entonces

ln (f (x)) = ln (g (x))

ln (e^{s i n (x^{2})}) = ln (f)

Aplicar las propiedades de los logaritmos:

ln (e^{a}) = a

ln (e^{s i n (x^{2})}) = sin (x^{2})

sin (x^{2}) = ln (f)

sin (x^{2}) = ln (f)

Aplicar propiedades trigonométricas inversas

sin (x^{2}) = ln (f)

Soluciones generales para

sin (x^{2}) = ln (f)

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x^{2} = arcsin (ln (f)) + 2 πn, x^{2} = π + arcsin (- ln (f)) + 2 πn

x^{2} = arcsin (ln (f)) + 2 πn, x^{2} = π + arcsin (- ln (f)) + 2 πn

Resolver

x^{2} = arcsin (ln (f)) + 2 πn : x = arcsin (ln (f)) + 2 πn, x = - arcsin (ln (f)) + 2 πn

x^{2} = arcsin (ln (f)) + 2 πn

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

x = arcsin (ln (f)) + 2 πn, x = - arcsin (ln (f)) + 2 πn

Resolver

x^{2} = π + arcsin (- ln (f)) + 2 πn : x = π + arcsin (- ln (f)) + 2 πn, x = - π + arcsin (- ln (f)) + 2 πn

x^{2} = π + arcsin (- ln (f)) + 2 πn

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

x = π + arcsin (- ln (f)) + 2 πn, x = - π + arcsin (- ln (f)) + 2 πn

x = arcsin (ln (f)) + 2 πn, x = - arcsin (ln (f)) + 2 πn, x = π + arcsin (- ln (f)) + 2 πn, x = - π + arcsin (- ln (f)) + 2 πn

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