What is 1/2 ln((x+1)/(x-1)) ?

The solution to 1/2 ln((x+1)/(x-1)) is 1/2 (ln(x+1)-ln(x-1))

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simplify 1/2 ln((x+1)/(x-1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

4 lo g_{10} (x) + 4 lo g_{10} (y)

4 lo g_{10} (x) - 6 lo g_{10} (y)

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

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

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

What is 1/2 ln((x+1)/(x-1)) ?
The solution to 1/2 ln((x+1)/(x-1)) is 1/2 (ln(x+1)-ln(x-1))