What is ln((x^3)/(sqrt(x^2+3))) ?

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

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simplify ln((x^3)/(sqrt(x^2+3)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 lo g_{5} (m) - 3 lo g_{5} (n)

\frac{1}{2} ln (x^{2} + 9) + ln (\frac{3}{x ^{2} + 9})

ln (3) + ln (2 x - 1) - ln (4) - ln (x + 1)

\frac{1}{2} ln (10 x)

ln (\frac{162}{e})

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