Find the solution to the equation 64^(3 – x) = 4^2x. Using complete sentences, explain the procedure used to solve this equation.

Question

anonymous · Answer

Let's start by stating that:
$$64=4^{3}$$
Now look at the problem:
$$64^{3-x}=4^{2x}$$
Substitute in the first statement:
$$4^{3(3-x)}=4^{2x}$$
$$4^{9-3x}=4^{2x}$$
Now we take the log base 4 on each side to remove the 4.
$$\log_{4} 4^{9-3x}=\log_{4} 4^{2x}$$
Taking the log base 4 cancels the 4 on each side so we get:
$$9-3x=2x$$
Now we simplify:
$$9=5x$$
$$x=\frac{9}{5}$$