What is ln((x^2)/(sin^3(x))) ?

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

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simplify ln((x^2)/(sin^3(x)))

simplify

ln (\frac{x ^{2}}{sin ^{3} ( x )})

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

Solution steps

ln (\frac{x ^{2}}{sin ^{3} ( x )})

Apply log rule:

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

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

= ln (x^{2}) - ln (sin^{3} (x))

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 ln (x) - ln (sin^{3} (x))

- 0.1 ln (0.1) - (1 - 0.1) ln (1 - 0.1)

- ln (2) + ln (3) + \frac{3}{2} ln (2)

ln (e^{x^{2}} x)

2 ln ∣ 2 ∣ - 2 ln \frac{1}{4}

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

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