What is ln((x^2+2x-9)/(x+3)) ?

The solution to ln((x^2+2x-9)/(x+3)) is ln(x^2+2x-9)-ln(x+3)

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simplify ln((x^2+2x-9)/(x+3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= ln (x^{2} + 2 x - 9) - ln (x + 3)

ln 5 + 2 - ln 5 - 2

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

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

ln (\frac{3}{4}) \cdot \frac{3}{4} + ln (\frac{1}{4}) \cdot \frac{1}{4}

0.3 \cdot ln (x) - ln (x + 3)

What is ln((x^2+2x-9)/(x+3)) ?
The solution to ln((x^2+2x-9)/(x+3)) is ln(x^2+2x-9)-ln(x+3)