which expressions are equivalent to 2 ln a + 2 ln b - ln a? check all that apply. ln ab² - ln a ln a + 2 ln…

which expressions are equivalent to 2 ln a + 2 ln b - ln a? check all that apply. ln ab² - ln a ln a + 2 ln b ln a² + ln b² - ln a 2 ln ab ln ab² done

which expressions are equivalent to 2 ln a + 2 ln b - ln a? check all that apply. ln ab² - ln a ln a + 2 ln b ln a² + ln b² - ln a 2 ln ab ln ab² done

Answer

Explanation:

Step1: Aplicar la propiedad de logaritmos $n\ln x=\ln(x^n)$

$2\ln a + 2\ln b-\ln a=\ln(a^2)+\ln(b^2)-\ln a$

Step2: Aplicar la propiedad $\ln x+\ln y = \ln(xy)$

$\ln(a^2)+\ln(b^2)-\ln a=\ln(a^2b^2)-\ln a$

Step3: Aplicar la propiedad $\ln x-\ln y=\ln(\frac{x}{y})$

$\ln(a^2b^2)-\ln a=\ln(\frac{a^2b^2}{a})=\ln(ab^2)$

Step4: Simplificar la expresión original de otra forma

$2\ln a + 2\ln b-\ln a=(2\ln a-\ln a)+ 2\ln b=\ln a + 2\ln b$

Answer:

  • $\ln a + 2\ln b$
  • $\ln a^2+\ln b^2-\ln a$
  • $\ln ab^2$