What is join tanh(1/2 ln((1+z)/(1-z))) ?

The solution to join tanh(1/2 ln((1+z)/(1-z))) is tanh(ln(((1+z)/(1-z))^{1/2}))

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join tanh(1/2 ln((1+z)/(1-z)))

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tanh (\frac{1}{2} ln (\frac{1 + z}{1 - z}))

tanh (ln ((\frac{1 + z}{1 - z})^{\frac{1}{2}}))

Solution steps

tanh (\frac{1}{2} ln (\frac{1 + z}{1 - z}))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (\frac{1 + z}{1 - z}) = ln ((\frac{1 + z}{1 - z})^{\frac{1}{2}})

= tanh (ln ((\frac{1 + z}{1 - z})^{\frac{1}{2}}))

2 lo g_{10} (2) + 4 lo g_{10} (3)

lo g_{10} (k) - 5 lo g_{10} (g)

lo g_{4} (5 x)

\frac{1}{2} ln (x) - \frac{2}{3} ln (y) - \frac{1}{4} ln (z)

ln (x - 3) + 2 ln (x)

What is join tanh(1/2 ln((1+z)/(1-z))) ?
The solution to join tanh(1/2 ln((1+z)/(1-z))) is tanh(ln(((1+z)/(1-z))^{1/2}))