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

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

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

simplify

ln (x - 1) + 2 ln (x + 1) - ln (2 x^{2})

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

Solution steps

ln (x - 1) + 2 ln (x + 1) - ln (2 x^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 ln (1 + u) + ln (x) - ln (u)

- ln (y + 1) - ln (x)

ln (\frac{469}{94.5})

ln (- 2 e^{x})

ln (e^{4 x} arctan (x^{2}))

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