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

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) (Show Source): You can put this solution on YOUR website!
ignoring for now, lets look at the other 2 equations.

We can take logs to the base2 with . First this is rewritten as . This then becomes

Now log2 to base2 is 1, so we get

--> 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... . We get 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.

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