Answer:
Option C. [tex]log_{2}135[/tex]
Step-by-step explanation:
The given expression is [tex]2log_{2}15-log_{2}5+log_{2}3[/tex]
We have to simplify this expression
[tex]2log_{2}15-log_{2}5+log_{2}3[/tex]
= [tex]log_{2}(15^{2})-log_{2}5+log_{2}3[/tex] [Since [tex]log(a^{n})=n(loga)[/tex]]
= [tex]log_{2}225-log_{2}5+log_{2}3[/tex]
=[tex]log_{2}\frac{225}{5}+log_{2}3[/tex] [Since [tex]log\frac{a}{b}=loga-logb[/tex]]
= [tex]log_{2}\frac{225\times 3}{5}[/tex] [Since [tex]log(a\times b)=loga+logb[/tex]]
= [tex]log_{2}135[/tex]
Therefore, Option C. [tex]log_{2}135[/tex] is the answer.
