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solvefor x,z=y^{sin(x)}

Solución

resolver para

x, z = y^{s i n (x)}

x = arcsin (\frac{ln ( z )}{ln ( y )}) + 2 πn, x = π + arcsin (- \frac{ln ( z )}{ln ( y )}) + 2 πn

Pasos de solución

z = y^{s i n (x)}

Intercambiar lados

y^{s i n (x)} = z

Aplicar las leyes de los exponentes

y^{s i n (x)} = z

f (x) = g (x)

, entonces

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

ln (y^{s i n (x)}) = ln (z)

Aplicar las propiedades de los logaritmos:

ln (x^{a}) = a \cdot ln (x)

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

sin (x) ln (y) = ln (z)

sin (x) ln (y) = ln (z)

Resolver

sin (x) ln (y) = ln (z) : sin (x) = \frac{ln ( z )}{ln ( y )}

sin (x) ln (y) = ln (z)

Dividir ambos lados entre

ln (y)

sin (x) ln (y) = ln (z)

Dividir ambos lados entre

ln (y)

\frac{sin ( x ) ln ( y )}{ln ( y )} = \frac{ln ( z )}{ln ( y )}

Simplificar

sin (x) = \frac{ln ( z )}{ln ( y )}

sin (x) = \frac{ln ( z )}{ln ( y )}

sin (x) = \frac{ln ( z )}{ln ( y )}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{ln ( z )}{ln ( y )}

Soluciones generales para

sin (x) = \frac{ln ( z )}{ln ( y )}

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

x = arcsin (\frac{ln ( z )}{ln ( y )}) + 2 πn, x = π + arcsin (- \frac{ln ( z )}{ln ( y )}) + 2 πn

x = arcsin (\frac{ln ( z )}{ln ( y )}) + 2 πn, x = π + arcsin (- \frac{ln ( z )}{ln ( y )}) + 2 πn

t, 10 = 14 + 8 sin (\frac{π t}{12})

cos (4 x) cos (x - 1) = 0

cos (0.5 t + 0.464) = 1

2 - 2 sin (θ) = 3

2 - 2 sin (θ) = 0