write log2(5) +log2​​​​​​​(3) in its simplest form

This is an exapmle of the addition rule as part of the logorithm syllabus. 

The general rule is log_ab + log_ac = log_a(b*c)

When the base of the logarithm is the same and they are added the to numbers of the logs may be multiplied therefore the answer to the problem would be log₂(5*3) = log₂15