Question

How do you solve `ln 3x = ln 15`?

Answer 1

`x=5`

Explanation:

In general if for some function
`color(white)("XXX")f(a) = (b)`
then one solution for `a` is `a=b`
and if for this same function `f(c)` is unique for `AAc`
then `a=b` is a unique solution.

`ln(a)` is a function of this form.

So
`color(white)("XXX")ln(3x) = ln(15)`
implies
`color(white)("XXX")3x=15`

Dividing both sides by 3 gives
`color(white)("XXX")x=5`