What is ln((4x^2+5x+4)/(x^{5/6)tan(x)}) ?

The solution to ln((4x^2+5x+4)/(x^{5/6)tan(x)}) is ln(4x^2+5x+4)-5/6 ln(x)-ln(tan(x))

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simplify ln((4x^2+5x+4)/(x^{5/6)tan(x)})

simplify

ln (\frac{4 x ^{2} + 5 x + 4}{x ^{\frac{5}{6}} tan ( x )})

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

Solution steps

ln (\frac{4 x ^{2} + 5 x + 4}{x ^{\frac{5}{6}} tan ( x )})

Apply log rule:

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

ln (\frac{4 x ^{2} + 5 x + 4}{x ^{\frac{5}{6}} tan ( x )}) = ln (4 x^{2} + 5 x + 4) - ln (x^{\frac{5}{6}} tan (x))

= ln (4 x^{2} + 5 x + 4) - ln (x^{\frac{5}{6}} tan (x))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x^{\frac{5}{6}} tan (x)) = ln (x^{\frac{5}{6}}) + ln (tan (x))

= ln (4 x^{2} + 5 x + 4) - (ln (x^{\frac{5}{6}}) + ln (tan (x)))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{\frac{5}{6}}) = \frac{5}{6} ln (x)

= ln (4 x^{2} + 5 x + 4) - (\frac{5}{6} ln (x) + ln (tan (x)))

- (\frac{5}{6} ln (x) + ln (tan (x))) : - \frac{5}{6} ln (x) - ln (tan (x))

= ln (4 x^{2} + 5 x + 4) - \frac{5}{6} ln (x) - ln (tan (x))

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ln (x) - ln (4)

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What is ln((4x^2+5x+4)/(x^{5/6)tan(x)}) ?
The solution to ln((4x^2+5x+4)/(x^{5/6)tan(x)}) is ln(4x^2+5x+4)-5/6 ln(x)-ln(tan(x))