What is join tanh(1/2 log_{10}((1+z)/(1-z))) ?

The solution to join tanh(1/2 log_{10}((1+z)/(1-z))) is tanh(log_{10}(((1+z)/(1-z))^{1/2}))

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join tanh(1/2 log_{10}((1+z)/(1-z)))

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tanh (\frac{1}{2} lo g_{10} (\frac{1 + z}{1 - z}))

tanh (lo g_{10} ((\frac{1 + z}{1 - z})^{\frac{1}{2}}))

Solution steps

tanh (\frac{1}{2} lo g_{10} (\frac{1 + z}{1 - z}))

Apply log rule:

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

\frac{1}{2} lo g_{10} (\frac{1 + z}{1 - z}) = lo g_{10} ((\frac{1 + z}{1 - z})^{\frac{1}{2}})

= tanh (lo g_{10} ((\frac{1 + z}{1 - z})^{\frac{1}{2}}))

\frac{1}{2} lo g_{10} (x) + \frac{1}{2} lo g_{10} (y)

lo g_{10} (\frac{27 a}{b})

ln (\frac{x}{x - 4}) + ln (\frac{x + 4}{x}) - ln (x^{2} - 16)

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

ln (4 x^{2})

What is join tanh(1/2 log_{10}((1+z)/(1-z))) ?
The solution to join tanh(1/2 log_{10}((1+z)/(1-z))) is tanh(log_{10}(((1+z)/(1-z))^{1/2}))