What is ln((4x^2+4x+8)/(x^{4/3)tan(x)}) ?

The solution to ln((4x^2+4x+8)/(x^{4/3)tan(x)}) is ln(4x^2+4x+8)-4/3 ln(x)-ln(tan(x))

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simplify ln((4x^2+4x+8)/(x^{4/3)tan(x)})

simplify

ln (\frac{4 x ^{2} + 4 x + 8}{x ^{\frac{4}{3}} tan ( x )})

ln (4 x^{2} + 4 x + 8) - \frac{4}{3} ln (x) - ln (tan (x))

Solution steps

ln (\frac{4 x ^{2} + 4 x + 8}{x ^{\frac{4}{3}} tan ( x )})

Apply log rule:

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

ln (\frac{4 x ^{2} + 4 x + 8}{x ^{\frac{4}{3}} tan ( x )}) = ln (4 x^{2} + 4 x + 8) - ln (x^{\frac{4}{3}} tan (x))

= ln (4 x^{2} + 4 x + 8) - ln (x^{\frac{4}{3}} tan (x))

Apply log rule:

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

ln (x^{\frac{4}{3}} tan (x)) = ln (x^{\frac{4}{3}}) + ln (tan (x))

= ln (4 x^{2} + 4 x + 8) - (ln (x^{\frac{4}{3}}) + ln (tan (x)))

Apply log rule:

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

ln (x^{\frac{4}{3}}) = \frac{4}{3} ln (x)

= ln (4 x^{2} + 4 x + 8) - (\frac{4}{3} ln (x) + ln (tan (x)))

- (\frac{4}{3} ln (x) + ln (tan (x))) : - \frac{4}{3} ln (x) - ln (tan (x))

= ln (4 x^{2} + 4 x + 8) - \frac{4}{3} ln (x) - ln (tan (x))

\frac{1}{4} ln (\frac{5}{3}) + \frac{1}{4} ln (5)

20 lo g_{10} (\frac{P}{2 \cdot 1 0 ^{- 4}})

\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣

- ln (3) + ln (2) + ln (2) - ln (1)

ln (p) + ln (1 - p)

What is ln((4x^2+4x+8)/(x^{4/3)tan(x)}) ?
The solution to ln((4x^2+4x+8)/(x^{4/3)tan(x)}) is ln(4x^2+4x+8)-4/3 ln(x)-ln(tan(x))