What is ln(x^2-3x-4)-ln(x-4)+ln(x+1) ?

The solution to ln(x^2-3x-4)-ln(x-4)+ln(x+1) is 2ln(x+1)

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simplify ln(x^2-3x-4)-ln(x-4)+ln(x+1)

simplify

ln (x^{2} - 3 x - 4) - ln (x - 4) + ln (x + 1)

2 ln (x + 1)

Solution steps

ln (x^{2} - 3 x - 4) - ln (x - 4) + ln (x + 1)

Apply log rule:

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

ln (x^{2} - 3 x - 4) - ln (x - 4) = ln (\frac{x ^{2} - 3 x - 4}{x - 4})

= ln (\frac{x ^{2} - 3 x - 4}{x - 4}) + ln (x + 1)

Simplify

\frac{x ^{2} - 3 x - 4}{x - 4} : x + 1

= ln (x + 1) + ln (x + 1)

Add similar elements:

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

= 2 ln (x + 1)

lo g_{4} (13 b^{2} c)

ln (2 \cdot 3)

ln (x^{2} - 5 x + 6) - ln (x^{2} - 4) + ln (x + 2)

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x) - lo g_{2} (3)

What is ln(x^2-3x-4)-ln(x-4)+ln(x+1) ?
The solution to ln(x^2-3x-4)-ln(x-4)+ln(x+1) is 2ln(x+1)