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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{2} ln (11)

lo g_{7} (\frac{f}{12})

\frac{1}{2} ln (12)

lo g_{4} (\frac{64}{x + 5})

(570 (10.5)) ln (\frac{1.5}{10.5})

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