You need to put your reindeer, Lancer, Prancer, Gloopin, and Bloopin, in a single-file line to pull your sleigh. However, Prancer and Lancer are fighting, so you have to keep them apart, or they won't fly. How many ways can you arrange your reindeer?

12 ways

Step-by-step explanation:

Normally there are 4 species of deer in the reindeer, which normally could have been arranged in 4! ways = 24 ways

Now considering the restriction that Prancer and Lancer are put apart

The number of arrangement when they are apart = Total number of ways - number of ways when they are together

Note: If they are put together, the two are seen as one which makes the arrangement to be 3!, but also note that either of them can be at the front or back.

Therefore, the number of arrangement when Prancer and Lancer are put together = 2(3!) = 2(3*2*1) = 12 ways

The number of arrangement when they are put apart = 24 - 12 = 12 ways

28

step-by-step explanation:

8+8+6+6

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)