SOLUTION: Y=2^(x+1) Y=4^(-x) find exact solution to system Answer is {{{x=1/3}}}, {{{drawing(200,50,-1,8,-1,2, locate(0,1,Y= 2^(2/3) ) )}}} How do you do it?

Algebra ->  Systems-of-equations -> SOLUTION: Y=2^(x+1) Y=4^(-x) find exact solution to system Answer is {{{x=1/3}}}, {{{drawing(200,50,-1,8,-1,2, locate(0,1,Y= 2^(2/3) ) )}}} How do you do it?      Log On


   

Question 365436: Y=2^(x+1)
Y=4^(-x)
find exact solution to system

Answer is
x=1%2F3,
drawing%28200%2C50%2C-1%2C8%2C-1%2C2%2C+locate%280%2C1%2CY=+2%5E%282%2F3%29+%29+%29


How do you do it?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
system%28Y=2%5E%28x%2B1%29%2C+Y=4%5E%28-x%29%29
2%5E%28x%2B1%29=4%5E%28-x%29 because both equal to Y
Write 4 as 2%5E2
2%5E%28x%2B1%29=%282%5E2%29%5E%28-x%29
Remove the parentheses on the right by multiplying exponents:
2%5E%28x%2B1%29=2%5E%28-2x%29
Use the principle:
If A%5EP=A%5EQ and A is positive and not equal to 1, then P=Q
Since 2 is positive and not equal to 1, we can equate the exponents:
x%2B1=-2x
3x=-1
x=-1%2F3
Substituting in either of the two original equations
system%28Y=2%5E%28x%2B1%29%2C+Y=4%5E%28-x%29%29

Checking by substituting in the other one:
Y=4%5E%28-%28-1%2F3%29%29+=+4%5E%281%2F3%29+=+%282%5E2%29%5E%281%2F3%29+=+2%5E%282%2F3%29
So the solution is
x=1%2F3,
drawing%28200%2C50%2C-1%2C8%2C-1%2C2%2C+locate%280%2C1%2CY=+2%5E%282%2F3%29+%29+%29

Edwin