Question

log2 6+log2 a=log2 14

Answer 1

6+a=14..........a=8

Answer 2

The reason people use logarithms is because you can add instead of multiply.
In other words
log(A B) = log(A) + log(B)
Here
\[\log_2 6 + \log_2 a= \log_2 14\]
\[\log_2 6a = \log_2 14\]
exponentiate both sides
6 a = 14
a= 14/6 = 7/3
See http://www.wolframalpha.com/input/?i=solve+log2+6%2Blog2+a%3Dlog2+14