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)

lo g_{4} (\frac{( a ^{2} \cdot b ^{3} )}{c \cdot d})

lo g_{10} (2) - lo g_{10} (3 i)

- 0.6 \cdot lo g_{2} (0.6) - 0.3 \cdot lo g_{2} (0.3)

- 4 \cdot ln (\frac{25}{13}) - 5 \cdot ln (\frac{25}{13})

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

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))