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

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

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

simplify

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

ln (\frac{x + 3}{x + 1})

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

= ln (\frac{x + 3}{x + 1})

ln (8) - 2 ln (4) + ln (15)

ln (27) - ln (9)

\frac{3}{2} lo g_{10} (5)

ln (3 x) - ln (x - 4)

ln (\frac{1 + y ^{2}}{x ^{2} + x y})

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