Respuesta :
Answer:
True:
[tex]\log (AB) = \log(A) + \log(B)\\\\\log(\sqrt{A}) = \dfrac{1}{2}\log(A)[/tex]
Step-by-step explanation:
1.
[tex]\ln(A) \ln(B) =\ln(A) + \ln(B)[/tex]
Correct property:
[tex]\log(AB) =\log(A) + \log(B)[/tex]
The given property is not true.
2.
[tex]\dfrac{\log (A)}{\log (B)} = \log(A)-\log(B)[/tex]
Correct property:
[tex]\log(\dfrac{A}{B}) = \log(A)-\log(B)[/tex]
the given property is not true.
3.
[tex]\log (AB) = \log(A) + \log(B)[/tex]
The given property is true.
4.
[tex]\log(\sqrt{A}) = \dfrac{1}{2}\log(A)[/tex]
The given property is true.
Property:
[tex]\log(A^p) = p\log(A)[/tex]
Using logarithm properties, it is found that the correct options are:
3. [tex]\log{(AB)} = \log{A} + \log{B}[/tex]
4. [tex]\log{\sqrt{A}} = \frac{1}{2}\log{A}[/tex]
The logarithm of the product is the sum of the logarithms, that is:
[tex]\log{(AB)} = \log{A} + \log{B}[/tex]
- Hence, option 3 is correct, while options 1 and 2 are incorrect.
The logarithm of power property is as follows:
[tex]\log{a^x} = x\log{a}[/tex]
Considering that [tex]\sqrt{A} = A^{\frac{1}{2}}[/tex], we have that:
[tex]\log{\sqrt{A}} = \frac{1}{2}\log{A}[/tex]
Hence option 4 is correct.
A similar problem is given at https://brainly.com/question/2620660
