A. x = –4 b. x = –13 c. x = –8 d. x = 14 15. a plane traveled from california and back. it took one hour longer on the way out than it did on the way back. the plane's average speed out was 300 mph. the average speed on the way back was 350 mph. how many hours did the trip out take? a. 6 hours b. 8 hours c. 7 hours d. 13 hours 16. solve y = log3243. a. y = 0 b. y = 3 c. y = 5 d. y = 243 17. solve 32x+3 = 243 for x. a. x = 2 b. x = 1 c. x = 2/5 d. x = 10 18. you have a photo that measures 1 in. wide by 3 in. tall. if you want to enlarge the photo so that the height is 18 in., what will the width of the photo be? a. 108 in. b. 4 in. c. 98 in. d. 6 in. 19. what is the value of x in the drawings if we know the triangles are similar? a. 36 ft. b. 12 ft. c. 30 ft. d. 18 ft. 20. solve the following equation for x: 64 = 23x. a. x = 2.5 b. x = 2 c. x = 1 d. x = 3

Please, please, post only ONE question at a time.  The way is set up, it's very difficult to conclude one problem and then move on to the next in the same session.

Solve y = log3243.  I must make the assumption here that you mean:

Solve y = (log to the base 3) of 243.

Solve y = (log   243   in better, more compact form.
                      3

If you recognize that 243 is an integer power of 3, the problem becomes much easier.  
                  2             3            4                  5
Note that 3   = 9,    3   = 27, 3   =81, and 3   = 243.

Also note that the log function and the exponential function are inverses of one another, and that inverse functions "undo" each other.
                      x
Thus, log    3     is simply x.
               3
                                           5
Thus, log    243  =  log     3    = 5 (answer).
                3                   3

Please repost the rest of your questions, one at a time, and then I will gladly help you with them.

The building is approximately 39 m high.

Step-by-step explanation:

As seen in the diagram attached, a triangle can be formed between the boy, the top of the building, and the lateral distance between the boy and the building.

We can now use trigonometric laws to find the distance AC between the boy's head and the top of the building.

tan 40 = AC/37.5

AC = 37.5 X tan 40 = 31.46m

We have just obtained the distance from the boy's head to the building top.

To get the true height of the building, we have to add the height of the platform the boy is standing on to the value just found.

7.5m + 31.46m = 39m