Question

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or multipal of logarithms.See example 3.

In 3x(x + 1)/(2x + 1)^2

Answer 1

`ln((3x))+ln((x+1))-2ln((2x+1))`

Explanation:

we need to keep in mind two properties of log:

• 
  `ln(ab)=ln(a)+ln(b)`

• 
  `\ln{(a)/(b)}=ln(a)-ln(b)`
• 
  `ln(a^b)=bln(a)`

`\ln{(3x(x+1))/((2x+1)^2)}`

`\ln{\left((3x(x+1))/((2x+1)^2)\right)}\\ln((3x(x+1)))-ln(((2x+1)^2))\\ln((3x))+ln((x+1))-ln(((2x+1)^2))`

`ln((3x))+ln((x+1))-2ln((2x+1))`

this is the rewritten expression!