What is ln((4x^4+4x)/(x^2+2x)) ?

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

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simplify ln((4x^4+4x)/(x^2+2x))

simplify

ln (\frac{4 x ^{4} + 4 x}{x ^{2} + 2 x})

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

Solution steps

ln (\frac{4 x ^{4} + 4 x}{x ^{2} + 2 x})

Apply log rule:

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

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

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

- (\frac{5}{6}) lo g_{2} (\frac{5}{6}) - (\frac{1}{6}) lo g_{2} (\frac{1}{6})

ln (\frac{2}{6})

3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

4 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

ln (5) + ln (7)

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