What is ln((\sqrt[4]{(a+1)(a-1)})/(a^2(a+3)^3)) ?

The solution to ln((\sqrt[4]{(a+1)(a-1)})/(a^2(a+3)^3)) is ln(\sqrt[4]{(a+1)(a-1)})-2ln(a)-3ln(a+3)

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simplify ln((\sqrt[4]{(a+1)(a-1)})/(a^2(a+3)^3))

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

ln (a^{2} (a + 3)^{3}) = ln (a^{2}) + ln ((a + 3)^{3})

Apply log rule:

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

ln (a^{2}) = 2 ln (a)

Apply log rule:

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

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

- (2 ln (a) + 3 ln (a + 3)) : - 2 ln (a) - 3 ln (a + 3)

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

\frac{2 ln ( 5 ) - 10 ln ( 9 )}{7 ln ( 5 ) - 2 ln ( 9 )}

\frac{ln ( 7 )}{2 ln ( 3 ) - ln ( 7 )}

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

lo g_{14} (\frac{14}{y})

What is ln((\sqrt[4]{(a+1)(a-1)})/(a^2(a+3)^3)) ?
The solution to ln((\sqrt[4]{(a+1)(a-1)})/(a^2(a+3)^3)) is ln(\sqrt[4]{(a+1)(a-1)})-2ln(a)-3ln(a+3)