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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 1)^{3}) = 3 ln (x + 1)

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

Apply log rule:

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

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

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

ln ((x + sin (x)) (x - sin (x)))

ln (\frac{( 3 x - 1 ) ^{3} ( x + 3 ) ^{4}}{( y - 6 ) ^{5}})

lo g_{10} (\frac{9}{4})

- lo g_{10} (5.98 \cdot 1 0^{- 4})

- 4 + 4 lo g_{e} (\frac{3}{4 e})

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