SOLUTION: If y = 9, find the integral values of x and z that satisfy all of the following equations: z^x = y^2x 2^z = (2)(4^x) x+y+z = 16 I'd really appreciate the help! Thanks in adva

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If y = 9, find the integral values of x and z that satisfy all of the following equations: z^x = y^2x 2^z = (2)(4^x) x+y+z = 16 I'd really appreciate the help! Thanks in adva      Log On


   

Question 26344: If y = 9, find the integral values of x and z that satisfy all of the following equations:
z^x = y^2x
2^z = (2)(4^x)
x+y+z = 16
I'd really appreciate the help! Thanks in advance.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
ignoring z%5Ex+=+y%5E2x for now, lets look at the other 2 equations.

We can take logs to the base2 with 2%5Ez+=+%282%29%284%5Ex%29. First this is rewritten as 2%5Ez+=+%282%29%282%5E%282x%29%29. This then becomes zlog2+=+log2+%2B+2xlog2

Now log2 to base2 is 1, so we get

z+=+1+%2B+2x
--> 2x - z = -1

x+y+z = 16
x+9+z = 16
--> x + z = 7

Add these 2 equations together and we get 3x = 6. Therefore x = 2.

Hence, from x+z = 7, we then know that z = 5.

So, we have x=2, z=5. Check these values in both of the original equations 2 and 3.

Now check in equation 1... z%5Ex+=+y%5E2x. We get 5%5E2+=+9%5E4 ie 25 = 6561 which is clearly wrong. So either you copied one of the equations down wrong? or the answer is "there is no solution to all 3 equations".

jon.