What is the general solution for 5^{5-3csc(θ)}=1 ?

The general solution for 5^{5-3csc(θ)}=1 is θ=0.64350…+2pin,θ=pi-0.64350…+2pin

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5^{5-3csc(θ)}=1

5^{5 - 3 c s c (θ)} = 1

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

Solution steps

5^{5 - 3 c s c (θ)} = 1

Apply exponent rules

(5 - 3 csc (θ)) ln (5) = ln (1)

Solve

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

csc (θ) = \frac{5}{3}

Apply trig inverse properties

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

Show solutions in decimal form

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

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

2 cos (θ) - 2 cos (3 θ) = 0

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

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

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

What is the general solution for 5^{5-3csc(θ)}=1 ?
The general solution for 5^{5-3csc(θ)}=1 is θ=0.64350…+2pin,θ=pi-0.64350…+2pin