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

tan (x) = - 1.5

2 cos^{2} (x) + cos (x) - 3 = 0

5 sin (θ) tan (θ) - 10 tan (θ) + 3 sin (θ) - 6 = 0

3 cos^{2} (θ) + 6 cos (θ) - 4 = 0

arccos (x) = 1

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}