Algebraically, how do you determine the intersection point of the functions #y=(1/2)^(-14x+1)# and #y=8^(2x+1)#?

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Answer 1 · 2017-01-04T03:17:02

#(1/2, 64)# is the point of intersection.

Solve through substitution.

#y= (1/2)^(-14x+ 1) -> (1/2)^(-14x + 1) = 8^(2x + 1)#

Write in equivalent bases.

#(2^-1)^(-14x + 1) = (2^3)^(2x + 1)#

#2^(14x - 1) = 2^(6x + 3)#

Eliminate the bases since they're now equivalent.

#14x - 1 = 6x + 3#

#14x - 6x = 3 + 1#

#8x= 4#

#x= 1/2#

Now input this value of #x# into one of the equations:

#y= 8^(2(1/2) + 1)#

#y = 8^2#

#y = 64#

Hopefully this helps!