What is ln((x-1)^{1/2})+ln((x+1)^{(-3)/2}) ?

The solution to ln((x-1)^{1/2})+ln((x+1)^{(-3)/2}) is ln(((x-1)/((x+1)^3))^{1/2})

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simplify ln((x-1)^{1/2})+ln((x+1)^{(-3)/2})

simplify

ln ((x - 1)^{\frac{1}{2}}) + ln ((x + 1)^{\frac{- 3}{2}})

ln (\frac{x - 1}{( x + 1 ) ^{3}})^{\frac{1}{2}}

Solution steps

ln ((x - 1)^{\frac{1}{2}}) + ln ((x + 1)^{\frac{- 3}{2}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((x - 1)^{\frac{1}{2}}) + ln ((x + 1)^{\frac{- 3}{2}}) = ln ((x + 1)^{\frac{- 3}{2}} (x - 1)^{\frac{1}{2}})

= ln ((x - 1)^{\frac{1}{2}} (x + 1)^{\frac{- 3}{2}})

Simplify

(x - 1)^{\frac{1}{2}} (x + 1)^{\frac{- 3}{2}} : (\frac{x - 1}{( x + 1 ) ^{3}})^{\frac{1}{2}}

= ln (\frac{x - 1}{( x + 1 ) ^{3}})^{\frac{1}{2}}

10 lo g_{10} (- 200 x)

- lo g_{10} (8.5 \cdot 1 0^{- 6})

2.4 ln (3) + ln (2)

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 8))

6 ln (\frac{a}{5}) + 4 ln (7 b)

What is ln((x-1)^{1/2})+ln((x+1)^{(-3)/2}) ?
The solution to ln((x-1)^{1/2})+ln((x+1)^{(-3)/2}) is ln(((x-1)/((x+1)^3))^{1/2})