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

1 Answer
Dec 9, 2015

Answer:

#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.