Question

Expand: In 2a^3/b^4

In 2 + 3 In a - 4 In b
In 2 - 3 In a - 4 In b
In 2 - 3 In a + 4 In b

Answer 1

ln(2) +3ln(a) -4ln(b)

Explanation:

`\ln{\left((2a^3)/(b^4)\right)}=\ln{(2a^3b^(-4))}=ln((2))+ln((a^3))+\ln{(b^(-4))}\\\\=\boxed{ln((2))+3ln((a))-4ln((b))}`

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The applicable rules of logarithms are ...

log(ab) = log(a)+log(b)

log(a^b) = b·log(a)