Mathematico | Mathematico

The function $f$ is defined by

f (x) = 8^{x} - 7 \times 4^{x} + 7 \times 2^{x + 1} - 8

Below, the curve $y = f (x)$ is sketched:

Given curve

Find the coordinates of all points of intersection between $C$ and the $x$ axis.

8^{x} = {(2^{x})}^{3}

and

4^{x} = {(2^{x})}^{2}

7 \times 2^{x + 1} = 14 \times 2^{x}

This is a cubic in disguise! Let $u = 2^{x}$ . You have a factor so you can use long division.