Write as a single logarithmic function: ln(x^2-4) - ln(x+2) + 2ln(x)

Question

Can you show the steps of how you get this answer... Thank you.

Answer 1

ln(x² - 4) - ln(x + 2) + 2ln(x)

 

 

Use the properties of logs. 

 

The coefficient of the log becomes the exponent of the argument.

 

ln(x² - 4) - ln(x + 2) + ln(x²)

 

 

When we subtract logs of common bases, we can divide the arguments.  When we add logs of common bases, we can multiply the arguments. 

 

 

ln[((x² - 4) / (x + 2)) * x²] =

 

ln[((x + 2)(x - 2) / (x + 2)) * x²] =

 

ln(x²(x - 2)) =

 

ln(x³ - 2x²)