What is 3ln|x|-4ln|x+1| ?

The solution to 3ln|x|-4ln|x+1| is ln((|x|^3)/((x+1)^4))

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simplify 3ln|x|-4ln|x+1|

simplify

3 ln ∣ x ∣ - 4 ln ∣ x + 1 ∣

ln (\frac{∣ x ∣ ^{3}}{( x + 1 ) ^{4}})

Solution steps

3 ln ∣ x ∣ - 4 ln ∣ x + 1 ∣

Apply log rule:

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

3 ln ∣ x ∣ = ln (∣ x ∣^{3})

= ln (∣ x ∣^{3}) - 4 ln ∣ x + 1 ∣

Apply log rule:

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

4 ln ∣ x + 1 ∣ = ln (∣ x + 1 ∣^{4})

= ln (∣ x ∣^{3}) - ln (∣ x + 1 ∣^{4})

Apply log rule:

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

ln (∣ x ∣^{3}) - ln (∣ x + 1 ∣^{4}) = ln (\frac{∣ x ∣ ^{3}}{∣ x + 1 ∣ ^{4}})

= ln (\frac{∣ x ∣ ^{3}}{∣ x + 1 ∣ ^{4}})

∣ x + 1 ∣^{4} = (x + 1)^{4}

= ln (\frac{∣ x ∣ ^{3}}{( x + 1 ) ^{4}})

ln ((4 x^{(2)} - 5) (2 x - 5)^{(3)})

\frac{1}{- 0.03794} ln (\frac{1}{76})

ln (x y) - 3

ln (\frac{16 e ^{- 42}}{( x + 1 ) ^{2}})

\frac{8.31 ( 310 )}{0.000995} ln (\frac{100}{5})

What is 3ln|x|-4ln|x+1| ?
The solution to 3ln|x|-4ln|x+1| is ln((|x|^3)/((x+1)^4))