Question

HElp with writing an expression as a single logarithm

Answer 1

\[\frac{ 5 }{ 6 }\log _{2}(x)+2/3\log _{2}(y)-1/2\log _{2}(x)-\log _{2}(y)\]
my professor said you should on the second part change the -log_{2}(y) to +log_{2}(y)
Is this correect?

Answer 2

Many people in my class thought itwouldbe wrong and just worked it out the other way. this is very confusing.

Answer 3

first, combine the similar terms we get :
5/6log_2 (x) + 2/3log_2 (y) − 1/2log_2 (x) − log_2 (y)
= 5/6log_2 (x) − 1/2log_2 (x) + 2/3log_2 (y) - log_2 (y)
= (5/6 - 1/2)log_2 (x) + (2/3 - 1)log_2 (y)
= -1/3log_2 (x) - 1/3log_2 (y)
then factor out and simplify
= -1/3 {log_2 (x) + log_2 (y)}
= -1/3 log_2 (xy)
= log_2 (xy)^(-1/3)
= log_2 1/(xy)^(1/3)