What is ln(x)+ln(x-4)+2ln(x+1) ?

The solution to ln(x)+ln(x-4)+2ln(x+1) is ln(x(x-4)(x+1)^2)

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simplify ln(x)+ln(x-4)+2ln(x+1)

simplify

ln (x) + ln (x - 4) + 2 ln (x + 1)

ln (x (x - 4) (x + 1)^{2})

Solution steps

ln (x) + ln (x - 4) + 2 ln (x + 1)

Apply log rule:

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

ln (x) + ln (x - 4) = ln (x (x - 4))

= ln (x (x - 4)) + 2 ln (x + 1)

Apply log rule:

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

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

= ln (x (x - 4)) + ln ((x + 1)^{2})

Apply log rule:

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

ln (x (x - 4)) + ln ((x + 1)^{2}) = ln (x (x + 1)^{2} (x - 4))

= ln (x (x - 4) (x + 1)^{2})

lo g_{10} (z^{2} x)

lo g_{3} (\frac{x ^{2} ( 2 x + 1 )}{x - 2})

10 ln (e^{- 5}) - lo g_{3} (\frac{1}{242})

2 lo g_{10} (x - y) - lo g_{10} (x + y)

ln (- 5 e^{- 5 x})

What is ln(x)+ln(x-4)+2ln(x+1) ?
The solution to ln(x)+ln(x-4)+2ln(x+1) is ln(x(x-4)(x+1)^2)