What is simplify-1/2 ln(x-1)-4/(x-1)+1/2 ln(x+1) ?

The solution to simplify-1/2 ln(x-1)-4/(x-1)+1/2 ln(x+1) is ln(sqrt((x+1)/(x-1)))-4/(x-1)

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simplify-1/2 ln(x-1)-4/(x-1)+1/2 ln(x+1)

simplify

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

ln (\frac{x + 1}{x - 1}) - \frac{4}{x - 1}

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

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

ln (x + 6) + 3 ln (x - 9)

lo g_{e} (x y) - lo g_{e} (∣ x ∣)

9.26 + lo g_{10} (\frac{0.2}{0.23})

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

ln (4 e^{- 4})

What is simplify-1/2 ln(x-1)-4/(x-1)+1/2 ln(x+1) ?
The solution to simplify-1/2 ln(x-1)-4/(x-1)+1/2 ln(x+1) is ln(sqrt((x+1)/(x-1)))-4/(x-1)