To determine which of the given expressions is equivalent to [tex]\(\log \left(\frac{12}{5}\right)\)[/tex], let's use properties of logarithms, particularly the property dealing with the logarithm of a quotient.
The logarithm of a quotient, [tex]\(\log \left(\frac{a}{b}\right)\)[/tex], can be expressed as the difference of the logarithms of the numerator and the denominator:
[tex]\[
\log \left(\frac{a}{b}\right) = \log (a) - \log (b)
\][/tex]
Applying this property to the given expression [tex]\(\log \left(\frac{12}{5}\right)\)[/tex]:
[tex]\[
\log \left(\frac{12}{5}\right) = \log (12) - \log (5)
\][/tex]
Therefore, the correct expression equivalent to [tex]\(\log \left(\frac{12}{5}\right)\)[/tex] is:
[tex]\[
\log (12) - \log (5)
\][/tex]
Thus, the correct answer is:
A. [tex]\(\log (12) - \log (5)\)[/tex]
