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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

ln (50 x)

ln (n^{2} + k^{2}) - ln (n^{2})

2 ln (2) + 2 β + 2 ln (x) + 3 e^{β} x

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

- ln (\frac{33}{9})

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