What is ln((e^2-e^4)/(x^2+7x+6)) ?

The solution to ln((e^2-e^4)/(x^2+7x+6)) is ln(e^2-e^4)-ln(x^2+7x+6)

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simplify ln((e^2-e^4)/(x^2+7x+6))

simplify

ln (\frac{e ^{2} - e ^{4}}{x ^{2} + 7 x + 6})

ln (e^{2} - e^{4}) - ln (x^{2} + 7 x + 6)

Solution steps

ln (\frac{e ^{2} - e ^{4}}{x ^{2} + 7 x + 6})

Apply log rule:

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

ln (\frac{e ^{2} - e ^{4}}{x ^{2} + 7 x + 6}) = ln (e^{2} - e^{4}) - ln (x^{2} + 7 x + 6)

= ln (- e^{4} + e^{2}) - ln (x^{2} + 7 x + 6)

3 lo g_{5} (u) + 7 lo g_{5} (v)

lo g_{b} (\frac{3}{7})

\frac{1}{4} ln (16) + \frac{1}{3} ln (125)

lo g_{5} (x) - lo g_{5} (x + 2)

What is ln((e^2-e^4)/(x^2+7x+6)) ?
The solution to ln((e^2-e^4)/(x^2+7x+6)) is ln(e^2-e^4)-ln(x^2+7x+6)