SteveIron
contestada

Which expressions are equivalent to
2 ln a + 2 ln b - ln a?

Check all that apply.

1. ln ab2 - ln a

2. ln a + 2 ln b

3. ln a2 + ln b2 - ln a

4. 2 ln ab

5. ln ab2

Respuesta :

The given expression is
2 ln a + 2 ln b - ln a
It simplifies to
ln a + ln b² = ln ab²

Let us check the given answers.
1. ln ab² - ln a   = ln (ab²)/a = ln b²
   FALSE

2. ln a + 2 ln b = ln ab²
   TRUE

3. ln a² + ln b² - ln a = ln (a²b²)/a = ln ab²
   TRUE

4. 2 ln ab = ln a²b²
   FALSE

5. ln ab²
   TRUE

Answer:
Choices 2, 3, and 5  are correct.

MrRoyal

Equivalent expressions are expressions with equal values

The equivalent expressions are: (2) ln a + 2 ln b,  (3) ln a2 + ln b2 - ln a and (5) ln ab2

The expression is given as:

2 ln a + 2 ln b - ln a

Collect like terms

2 ln a + 2 ln b - ln a = 2 ln a - ln a + 2 ln b

Evaluate the like terms

2 ln a + 2 ln b - ln a = ln a + 2 ln b

Also, we have:

2 ln a + 2 ln b - ln a = 2 ln a - ln a + 2 ln b

Apply law of logarithm

[tex]2\ln a + 2\ ln b - \ln a = \ln a^2 - \ln a + \ln b^2[/tex]

Apply law of logarithm

[tex]2\ln a + 2\ ln b - \ln a = \ln \frac{a^2 * b^2}{a}[/tex]

Simplify

[tex]2\ln a + 2\ ln b - \ln a = \ln ab^2[/tex]

Hence, the equivalent expressions are:

(2) ln a + 2 ln b,  (3) ln a2 + ln b2 - ln a and (5) ln ab2

Read more about equivalent expressions at:

https://brainly.com/question/2972832

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