Question

How do you condense `4 ln (x+4) - 5 ln x`?

Answer 1

`ln ((x+4)^4/x^5)`

Explanation:

To condense to a single log, we need to use the properties listed below

Sum to product: `log A + log B iff log(AB)`
Difference to quotient: `log A- log B iff log (A/B), B !=0`
Power rule: `logA^n iff n log A`

Given `4 ln(x+4) - 5 ln x`

Step 1: Reverse the power rule to get
`ln(x+4)^4 - ln(x)^5`

Step 2: Reverse the difference to quotient rule
`ln((x+4)^4/x^5)`

Now, you are done.