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

Answer:

$\ln{(3x)}+\ln{(x+1)}-2\ln{(2x+1)}$

Step-by-step explanation:

we need to keep in mind two properties of log:

• $\ln{ab}=\ln{a}+\ln{b}$

• $\ln{\dfrac{a}{b}}=\ln{a}-\ln{b}$
• $\ln{a^b}=b\ln{a}$

$\ln{\dfrac{3x(x+1)}{(2x+1)^2}}$

$\ln{\left(\dfrac{3x(x+1)}{(2x+1)^2}\right)}\\\ln{(3x(x+1))}-\ln{((2x+1)^2)}\\\ln{(3x)}+\ln{(x+1)}-\ln{((2x+1)^2)}$

$\ln{(3x)}+\ln{(x+1)}-2\ln{(2x+1)}$

this is the rewritten expression!