Question

Find the solution to the equation 64^(4 – x) = 4^2x. Using complete sentences, explain the procedure used to solve this equation.

Answer 1

First of all, we equate the bases. Then, we put up and equation of the exponents and solve for x.

Answer 2

\(\Large \color{MidnightBlue}{\Rightarrow (4^3)^{4 - x} = 4^{2x} }\)

\(\Large \color{MidnightBlue}{\Rightarrow 4^{12 - 3x} = 4^{2x} }\)

\(\Large \color{MidnightBlue}{\Rightarrow 12 - 3x = 2x }\)

\(\Large \color{MidnightBlue}{\Rightarrow 12 = 5x }\)

\(\Large \color{MidnightBlue}{\Rightarrow x = {6 \over 5} }\)