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

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

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

simplify

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

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

Solution steps

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

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}) + 2 ln (x - 3) + c

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 ((x - 3)^{2}) + c

Apply log rule:

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

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

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

9 lo g_{135} (- 9 lo g_{5} (x))

ln (\frac{x ^{2} - 9}{x ^{3} + 27})

lo g_{10} (a ln (x))

- ln (x^{2}) - ln (sin (y))

ln (y) + ln (x + 1) - ln (k)

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