Aclerk has 4 different letters that need to go in 4 different envelopes. what is the probability that all 4 letters are placed in the correct envelopes?

1/4 * 1/3 * 1/2 * 1/1 = 1/24 chance that all 4 letters are placed in the correct envelopes.

With the first envelope, there are 4 choices of letters, so the probability of picking the correct letter is 1/4.

With the second envelope, there are 3 remaining letters, so the probability of picking the correct letter is 1/3.

The same logic follows the the third and final letter.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.