Question

Which of the following expressions is equivalent to the expression shown below?

Answer 1

$2\log_{2}{15}-\log_{2}{5}+\log_{2}{3}=\log_{2}{15^2}-\log_{2}{5}+\log_{2}{3}\\=\log_2{\frac{225\times3}{5}}=\log_2{135}$

Answer 2

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.