What is the general solution for 2arctanh((x-2)/(x+1))=ln(2) ?

The general solution for 2arctanh((x-2)/(x+1))=ln(2) is No Solution for x\in\mathbb{R}

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2arctanh((x-2)/(x+1))=ln(2)

2 arctanh (\frac{x - 2}{x + 1}) = ln (2)

No Solution for x \in R

Solution steps

2 arctanh (\frac{x - 2}{x + 1}) = ln (2)

Solve by substitution

arctanh (\frac{x - 2}{x + 1}) = \frac{ln ( 2 )}{2}

Subtract

ln (2)

from both sides

2 arctanh (\frac{x - 2}{x + 1}) - ln (2) = 0

Solve by substitution

arctanh (\frac{x - 2}{x + 1}) = \frac{ln ( 2 )}{2}

Rewrite using trig identities

- ln (2) + ln (\frac{- 1 + 2 x}{3}) = 0

Move

ln (2)

to the right side

ln (\frac{- 1 + 2 x}{3}) = ln (2)

Apply trig inverse properties

No Solution for x \in R

sec (β) = 3, \frac{3 π}{2} < β < 2 π

cos (x) = \frac{2.9}{3.2}

sin (θ) = \frac{3}{2}, 0 \leq θ < 2 π

cos (θ) sin (θ) - 3 cos (θ) = 0

\frac{3}{2} = cos (θ)

What is the general solution for 2arctanh((x-2)/(x+1))=ln(2) ?
The general solution for 2arctanh((x-2)/(x+1))=ln(2) is No Solution for x\in\mathbb{R}