What is 2ln(x-3)-ln(6)-3ln(x+2) ?

The solution to 2ln(x-3)-ln(6)-3ln(x+2) is ln(((x-3)^2)/(6(x+2)^3))

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simplify 2ln(x-3)-ln(6)-3ln(x+2)

simplify

2 ln (x - 3) - ln (6) - 3 ln (x + 2)

ln (\frac{( x - 3 ) ^{2}}{6 ( x + 2 ) ^{3}})

Solution steps

2 ln (x - 3) - ln (6) - 3 ln (x + 2)

Apply log rule:

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

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

= ln ((x - 3)^{2}) - ln (6) - 3 ln (x + 2)

Apply log rule:

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

ln ((x - 3)^{2}) - ln (6) = ln (\frac{( x - 3 ) ^{2}}{6})

= ln (\frac{( x - 3 ) ^{2}}{6}) - 3 ln (x + 2)

Apply log rule:

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

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

= ln (\frac{( x - 3 ) ^{2}}{6}) - ln ((x + 2)^{3})

Apply log rule:

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

ln (\frac{( x - 3 ) ^{2}}{6}) - ln ((x + 2)^{3}) = ln (\frac{\frac{( x - 3 ) ^{2}}{6}}{( x + 2 ) ^{3}})

= ln (\frac{\frac{( x - 3 ) ^{2}}{6}}{( x + 2 ) ^{3}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{( x - 3 ) ^{2}}{6 ( x + 2 ) ^{3}})

\frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x + 2 ∣

ln (\frac{x ^{2} y}{4 e ^{5} y ^{3}})

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

\frac{1}{0.04} ln (\frac{72}{72 - 42})

ln (\frac{y ^{x} \cdot e ^{- y}}{x !})

What is 2ln(x-3)-ln(6)-3ln(x+2) ?
The solution to 2ln(x-3)-ln(6)-3ln(x+2) is ln(((x-3)^2)/(6(x+2)^3))