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

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

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

simplify

ln (x) + 3 ln (x - 3) - 3 ln (x + 3)

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

Solution steps

ln (x) + 3 ln (x - 3) - 3 ln (x + 3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln ∣ 1 - 5 ∣ - ln ∣ 1 - 4 ∣ + 1

\frac{9}{2} - 9 ln (4) + 9 ln (3)

\frac{d ^{4}}{d x ^{4}} (e^{- 4 x}) + 6 ln (3 x^{5})

ln (y) - \frac{1}{2} ln (y - 1) - \frac{1}{2} ln (y + 1)

ln (\frac{\frac{1}{2}}{\frac{1}{4}})

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