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

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

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simplify ln((a^3)/((a+1)^2))

simplify

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

3 ln (a) - 2 ln (a + 1)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 3 ln (a) - 2 ln (a + 1)

ln (v) - ln (20)

- lo g_{10} (9.3 \cdot 1 0^{- 7})

ln ((ln (5 x))^{l n (3 x)})

ln (y + 1) + ln (y - 1)

- lo g_{10} (0.37 \cdot 1 0^{- 9})

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