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

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Answer 1 · 2015-12-09T06:28:14

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

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.

How do you condense 4 ln (x+4) - 5 ln x4 ln (x+4) - 5 ln x?