Combine the following log into one expression

Question

2ln(x-3)-1/2ln(x+1)-3ln(x²⁾

Answer 1

Sarah,

 

2 ln (x-3) - ½ ln (x+1) - 3 ln (x²) = ln (x-3)² - ln √(x+1) - ln (x²)³

 

   = ln (x-3)² - [ln √(x+1) + ln (x⁶)]

 

   = ln (x-3)² - ln [x⁶√(x+1)]

 

   = ln [(x-3)²/[x⁶√(x+1)]

 

I have left the reasons out and the explanation of the algebra steps I used along the way. If you have any further questions about how I did this, please post a reply as soon as necessary.