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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

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

2 ln (x) + 3 ln (x + 1)

ln (e (x - 8))

ln (a e^{b})

lo g_{2} (45) - lo g_{2} (5)

lo g_{2} (\frac{x ^{3} y}{5 z ^{6}})

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