What is the general solution for solvefor u,x=4tanh(u) ?

The general solution for solvefor u,x=4tanh(u) is u= 1/2 ln((x+4)/(4-x)),u=ln(-sqrt((x+4)/(4-x)))

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solvefor u,x=4tanh(u)

solve for

u, x = 4 tanh (u)

u = \frac{1}{2} ln (\frac{x + 4}{4 - x}), u = ln (- \frac{x + 4}{4 - x})

Solution steps

x = 4 tanh (u)

Switch sides

4 tanh (u) = x

Rewrite using trig identities

4 \cdot \frac{e ^{u} - e ^{- u}}{e ^{u} + e ^{- u}} = x

4 \cdot \frac{e ^{u} - e ^{- u}}{e ^{u} + e ^{- u}} = x : u = \frac{1}{2} ln (\frac{x + 4}{4 - x}), u = ln (- \frac{x + 4}{4 - x})

u = \frac{1}{2} ln (\frac{x + 4}{4 - x}), u = ln (- \frac{x + 4}{4 - x})

tan (x) = \frac{2}{7}

sin^{2} (θ) + cos (θ) - cos^{2} (θ) = 0

\frac{cos ( x )}{sin ( 2 x )} = \frac{5}{7}

tan (x) = \frac{6 \cdot 0.809}{15}

tan (θ) = \frac{8}{20}

What is the general solution for solvefor u,x=4tanh(u) ?
The general solution for solvefor u,x=4tanh(u) is u= 1/2 ln((x+4)/(4-x)),u=ln(-sqrt((x+4)/(4-x)))