Question

Why is `3*ln(x) = ln(x^3)`?

Answer 1

Use the definition of logarithm and basic properties of exponents.
(details below)

Explanation:

Basic definition:
`color(white)("XXX")ln(a)=b` means `e^b=a`

Let `s =3 ln(x)`
`color(white)("XXX")rArr ln(x)= s/3`

`color(white)("XXX")rArr e^(s/3) = x`

`color(white)("XXX")rArr root(3)(e^s) = x`

`color(white)("XXX")rArr e^s = x^3`

`color(white)("XXX")rArrln(x^3) = s`

`color(white)("XXX")rArrln(x^3) = 3ln(x)`