What is 1/2 log_{e}((1+x)/(1-x)) ?

The solution to 1/2 log_{e}((1+x)/(1-x)) is 1/2 (ln(1+x)-ln(1-x))

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simplify 1/2 log_{e}((1+x)/(1-x))

simplify

\frac{1}{2} lo g_{e} (\frac{1 + x}{1 - x})

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

Solution steps

\frac{1}{2} lo g_{e} (\frac{1 + x}{1 - x})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{e} (\frac{1 + x}{1 - x}) = lo g_{e} (1 + x) - lo g_{e} (1 - x)

= \frac{1}{2} (lo g_{e} (x + 1) - lo g_{e} (- x + 1))

Apply log rule:

lo g_{e} (x) = ln (x)

= \frac{1}{2} (ln (x + 1) - lo g_{e} (- x + 1))

Apply log rule:

lo g_{e} (x) = ln (x)

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

\frac{ln ( \frac{15}{2} )}{2 ln ( 2 )}

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

ln (\frac{x ^{6} - x}{x ^{3} + 2})

lo g_{5} (x^{4})

\frac{8.314 \cdot 310}{- 1 \cdot 96485} ln (\frac{119}{12})

What is 1/2 log_{e}((1+x)/(1-x)) ?
The solution to 1/2 log_{e}((1+x)/(1-x)) is 1/2 (ln(1+x)-ln(1-x))