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Popular >

5^{5-3csc(θ)}=1

Solución

5^{5 - 3 c s c (θ)} = 1

Solución

θ = 0.64350 \dots + 2 πn, θ = π - 0.64350 \dots + 2 πn

+1

Grados

θ = 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 143.13010 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

5^{5 - 3 c s c (θ)} = 1

Aplicar las leyes de los exponentes

5^{5 - 3 c s c (θ)} = 1

Si

f (x) = g (x)

, entonces

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

ln (5^{5 - 3 c s c (θ)}) = ln (1)

Aplicar las propiedades de los logaritmos:

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

ln (5^{5 - 3 c s c (θ)}) = (5 - 3 csc (θ)) ln (5)

(5 - 3 csc (θ)) ln (5) = ln (1)

(5 - 3 csc (θ)) ln (5) = ln (1)

Resolver

(5 - 3 csc (θ)) ln (5) = ln (1) : csc (θ) = \frac{5}{3}

(5 - 3 csc (θ)) ln (5) = ln (1)

Dividir ambos lados entre

ln (5)

(5 - 3 csc (θ)) ln (5) = ln (1)

Dividir ambos lados entre

ln (5)

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )} = \frac{ln ( 1 )}{ln ( 5 )}

Simplificar

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )} = \frac{ln ( 1 )}{ln ( 5 )}

Simplificar

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )} : 5 - 3 csc (θ)

\frac{( 5 - 3 csc ( θ ) ) ln ( 5 )}{ln ( 5 )}

Eliminar los terminos comunes:

ln (5)

= 5 - 3 csc (θ)

Simplificar

\frac{ln ( 1 )}{ln ( 5 )} : 0

\frac{ln ( 1 )}{ln ( 5 )}

Simplificar

ln (1) : 0

ln (1)

Aplicar las propiedades de los logaritmos:

lo g_{a} (1) = 0

= 0

= \frac{0}{ln ( 5 )}

Aplicar la regla

\frac{0}{a} = 0, a \neq = 0

= 0

5 - 3 csc (θ) = 0

5 - 3 csc (θ) = 0

5 - 3 csc (θ) = 0

Mover

5

al lado derecho

5 - 3 csc (θ) = 0

Restar

5

de ambos lados

5 - 3 csc (θ) - 5 = 0 - 5

Simplificar

- 3 csc (θ) = - 5

- 3 csc (θ) = - 5

Dividir ambos lados entre

- 3

- 3 csc (θ) = - 5

Dividir ambos lados entre

- 3

\frac{- 3 csc ( θ )}{- 3} = \frac{- 5}{- 3}

Simplificar

csc (θ) = \frac{5}{3}

csc (θ) = \frac{5}{3}

csc (θ) = \frac{5}{3}

Aplicar propiedades trigonométricas inversas

csc (θ) = \frac{5}{3}

Soluciones generales para

csc (θ) = \frac{5}{3}

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

θ = arccsc (\frac{5}{3}) + 2 πn, θ = π - arccsc (\frac{5}{3}) + 2 πn

θ = arccsc (\frac{5}{3}) + 2 πn, θ = π - arccsc (\frac{5}{3}) + 2 πn

Mostrar soluciones en forma decimal

θ = 0.64350 \dots + 2 πn, θ = π - 0.64350 \dots + 2 πn

Ejemplos populares

sin (z) = \frac{4}{7}

2cos(θ)-2cos(3θ)=0

2 cos (θ) - 2 cos (3 θ) = 0

5-7sin(A)-2cos^2(A)=0

5 - 7 sin (A) - 2 cos^{2} (A) = 0

solvefor x,ln(y)+y^2=sin(x)+c resolver para

x, ln (y) + y^{2} = sin (x) + c

5/2 =2+cos(x+(2pi)/3)

\frac{5}{2} = 2 + cos (x + \frac{2 π}{3})