What is ln((x(x^2+1)^2)/(sqrt(2x^3-1))) ?

The solution to ln((x(x^2+1)^2)/(sqrt(2x^3-1))) is ln(x)+2ln(x^2+1)-ln(sqrt(2x^3-1))

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simplify ln((x(x^2+1)^2)/(sqrt(2x^3-1)))

simplify

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

ln (x) + 2 ln (x^{2} + 1) - ln (2 x^{3} - 1)

Solution steps

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

Apply log rule:

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

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

= ln (x (x^{2} + 1)^{2}) - ln (2 x^{3} - 1)

Apply log rule:

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

ln (x (x^{2} + 1)^{2}) = ln (x) + ln ((x^{2} + 1)^{2})

= ln (x) + ln ((x^{2} + 1)^{2}) - ln (2 x^{3} - 1)

Apply log rule:

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

ln ((x^{2} + 1)^{2}) = 2 ln (x^{2} + 1)

= ln (x) + 2 ln (x^{2} + 1) - ln (2 x^{3} - 1)

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

lo g_{10} (\frac{40}{9}) + 4 lo g_{10} (5) + 2 lo g_{10} (6)

2 - lo g_{5} (\frac{1}{16}) - \frac{1}{3} lo g_{5} (8)

5 ln (x) + 4 ln (y) - 2 ln (z)

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

What is ln((x(x^2+1)^2)/(sqrt(2x^3-1))) ?
The solution to ln((x(x^2+1)^2)/(sqrt(2x^3-1))) is ln(x)+2ln(x^2+1)-ln(sqrt(2x^3-1))