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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{2} lo g_{7} (2)

ln (1.3 \cdot 1 0^{- 3})

lo g_{π} (\frac{505}{56})

ln (\frac{d}{x})

ln (3 x) + ln (7 x)

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