Log (base 2) 192 is equivalent to which statement(s):

a) log (base 2) 64 x log (base 2) 3 = 6log (base 2) 3

b) log (base 2) 64 + log (base 2) 3 = 6 + log (base 2) 3

c) log (base 2) 32 x log (base 2) 6 = 5log (base 2) 6

d) log (base 2) 32 + log (base 2) 6 = 5 + log (base 2) 6

e) log (bas 2) 8 x log (base 2) 24 = 3log (base 2) 24

f) log (base 2) 8 + log (base 2) 24 = 3 + log (base 2) 24

If there are multiple answers, separate each with a comma.

### 1 Answer | Add Yours

`log_2(192)=log_2(64*3)`

`=log_2(64)+log_2(3)` (using `log_a(m*n)=log_am+log_an` )

`=log_2(2^6)+log_2(3)`

`=6log_2(2)+log_2(3)` (using `log_am^n` =`nlog_am` )

`=6+log_2(3)`

Again, `log_2(192)=log_2(32*6)`

`=log_2(32)+log_2(6)`

`=log_2(2^5)+log_2(6)`

`=5log_2(2)+log_2(6)`

`=5+log_2(6)`

We can also write `log_2(192)=log_2(8*24)`

`=log_2(8)+log_2(24)`

`=log_2(2^3)+log_2(24)`

`=3log_2(2)+log_2(24)`

`=3+log_2(24)`

**Therefore, the correct options are b), d) and f).**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes