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