Answer:
[tex] \displaystyle A) 5\log( {x}^{} ) + 2 \log( {y}^{} ) [/tex]
Step-by-step explanation:
we would like to expand the following logarithmic expression:
[tex] \displaystyle \log( {x}^{5} {y}^{2} ) [/tex]
remember the multiplication logarithmic indentity given by:
[tex] \displaystyle \rm \log( \alpha \times \beta ) \iff \log( \alpha ) + \log( \beta ) [/tex]
so our given expression should be
[tex] \displaystyle \log( {x}^{5} ) + \log( {y}^{2} ) [/tex]
by exponent logarithmic property we acquire:
[tex] \displaystyle 5\log( {x}^{} ) + 2 \log( {y}^{} ) [/tex]
hence, our answer is A
