Answer :
To determine which of the provided expressions is equivalent to \(\ln 5 + \ln 3\), let's use logarithmic properties to simplify and analyze the expression step-by-step. Specifically, we will use the logarithm product rule, which states:
[tex]\[ \ln(a) + \ln(b) = \ln(a \cdot b) \][/tex]
Given the expression \(\ln 5 + \ln 3\), we apply the product rule as follows:
[tex]\[ \ln 5 + \ln 3 = \ln(5 \cdot 3) \][/tex]
Now, we calculate the product inside the logarithm:
[tex]\[ 5 \cdot 3 = 15 \][/tex]
Therefore, we can rewrite the expression as:
[tex]\[ \ln 5 + \ln 3 = \ln 15 \][/tex]
Hence, the equivalent expression is:
[tex]\[ \ln 15 \][/tex]
Among the given options, this corresponds to option C:
C. \(\ln 15\)
After verifying \(\ln 5 + \ln 3\) and finding the equivalent logarithmic expression to be \(\ln 15\), also we notice the numerical verification aligns:
- Both \(\ln 5 + \ln 3\) and \(\ln 15\) have the same numerical value, which reinforces our conclusion.
Therefore, the correct answer is:
C. [tex]\(\ln 15\)[/tex]
[tex]\[ \ln(a) + \ln(b) = \ln(a \cdot b) \][/tex]
Given the expression \(\ln 5 + \ln 3\), we apply the product rule as follows:
[tex]\[ \ln 5 + \ln 3 = \ln(5 \cdot 3) \][/tex]
Now, we calculate the product inside the logarithm:
[tex]\[ 5 \cdot 3 = 15 \][/tex]
Therefore, we can rewrite the expression as:
[tex]\[ \ln 5 + \ln 3 = \ln 15 \][/tex]
Hence, the equivalent expression is:
[tex]\[ \ln 15 \][/tex]
Among the given options, this corresponds to option C:
C. \(\ln 15\)
After verifying \(\ln 5 + \ln 3\) and finding the equivalent logarithmic expression to be \(\ln 15\), also we notice the numerical verification aligns:
- Both \(\ln 5 + \ln 3\) and \(\ln 15\) have the same numerical value, which reinforces our conclusion.
Therefore, the correct answer is:
C. [tex]\(\ln 15\)[/tex]
