Question

Part 1 [3 points]: Find the solution to the equation 64^(x - 4) = 4^2x.
Part 2 [4 points]: Use complete sentences to explain the method used to solve this equation.

Answer 1

64 = 4^3

so

\[64^{x - 4} = 4^{3(x - 4)}\]

equating powers since the same base

3(x -4) = 2x

3x - 12 = 2x

x = 12

Answer 2

take log of both sides
use log property: log( x^n) = n*log(x)

\[(x-4) \log 64 = 2x \log 4\]

Answer 3

or that :{

Answer 4

Thanks:)