What is simplify-3/2 ln|w^2+1|+3ln(w) ?

The solution to simplify-3/2 ln|w^2+1|+3ln(w) is ln((w^3)/(|w^2+1|^{3/2)})

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simplify-3/2 ln|w^2+1|+3ln(w)

simplify

- \frac{3}{2} ln w^{2} + 1 + 3 ln (w)

ln (\frac{w ^{3}}{∣ w ^{2} + 1 ∣ ^{\frac{3}{2}}})

Solution steps

- \frac{3}{2} ln w^{2} + 1 + 3 ln (w)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{2} ln w^{2} + 1 = ln (w^{2} + 1^{\frac{3}{2}})

= - ln (w^{2} + 1^{\frac{3}{2}}) + 3 ln (w)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (w) = ln (w^{3})

= - ln (w^{2} + 1^{\frac{3}{2}}) + ln (w^{3})

Apply log rule:

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

ln (w^{3}) - ln (w^{2} + 1^{\frac{3}{2}}) = ln (\frac{w ^{3}}{∣ w ^{2} + 1 ∣ ^{\frac{3}{2}}})

= ln (\frac{w ^{3}}{∣ w ^{2} + 1 ∣ ^{\frac{3}{2}}})

13 lo g_{10} (a) - 2 lo g_{10} (b) + lo g_{10} (c)

ln (4) + 2 ln (4^{2} + 4) - ln (1) + 2 ln (1^{2} + 4)

2 ln (2) + \frac{17 ln ( 2 ) - 9 ln ( 3 )}{5}

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

lo g_{2} (\frac{6 x ^{2}}{y z ^{3}})

What is simplify-3/2 ln|w^2+1|+3ln(w) ?
The solution to simplify-3/2 ln|w^2+1|+3ln(w) is ln((w^3)/(|w^2+1|^{3/2)})