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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

ln (x + 1) + ln (x - 1) = ln ((x + 1) (x - 1))

= ln (x) - ln ((x + 1) (x - 1))

Apply log rule:

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

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

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

- lo g_{10} (2.6 \cdot 1 0^{- 5})

ln (\frac{6 x}{y ^{2}})

ln (5 e^{- 2 x})

lo g_{10} (13) 13

ln (x (1 + x)^{5})

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