\(log_2\dfrac{2}{3}+log_212=log_2\left(\dfrac{2}{3}.12\right)=log_28=3\)
\(log_228-log_27=log_2\left(\dfrac{28}{7}\right)=log_24=2\)
\(log_327=log_33^3=3log_33=3\)
\(log_{32}2=log_{2^5}2=\dfrac{1}{5}log_22=\dfrac{1}{5}\)
\(log_381=log_33^4=4log_33=4\)
a) \(\log_2\dfrac{2}{3}+log_212=log_2\left(\dfrac{2}{3}.12\right)=log_28=3\)
b) \(log_228-log_27=log_2\left(\dfrac{28}{7}\right)=log_24=2\)
c) \(log_327=log_3\left(3^3\right)=3\)
d) \(log_{32}2=log_{2^5}2=\dfrac{1}{5}\)
e) \(log_381=log_3\left(3^4\right)=4\)