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!

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