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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

3 lo g_{a} (2) + lo g_{a} (c) - 2 lo g_{a} (d)

- lo g_{10} (1.25 \cdot 1 0^{- 10})

\frac{1}{2} ln (5) - \frac{1}{2} ln (2)

ln (5 e^{- 4 t})

0.026 ln (\frac{5 \cdot 1 0 ^{- 4}}{1 0 ^{- 12}})

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