Question

Part 1 Find the solution to the equation 64^(x – 4) = 4^2x.
Part 2 Use complete sentences to explain the method used to solve this equation.

Answer 1

Okay, so do you agree that \(\large (a^x)^y = a^{xy}\) to start with?

Answer 2

yes

Answer 3

So, do you agree that \(64^{x - 4}\) can be written as \((\large 4^3)^{x - 4} = {4^{3x - 12}}\)?

Answer 4

yes it can

Answer 5

Okay, so the equation has a follow-up like \(4^{2x} = 4^{3x - 12}\)

Answer 6

When two terms are equal, and the base is same, then the EXPONENT MUST BE THE SAME.

Answer 7

So we can write a new equation:

\( \color{Black}{\Rightarrow 2x = 3x - 12}\)
We solve it by subtracting 3x.
\( \color{Black}{\Rightarrow -x = -12 }\)

\( \color{Black}{\Rightarrow x = 12}\)

Answer 8

Did you understand?

Answer 9

I understood it soooo much better thank you so much for your help!!!!