Question

find the solution to the equation 64^(x - 3) = 4^2x

Answer 1

\[\large \Rightarrow 64^{(x-3)} = 4^{2x}\] \[\large \Rightarrow 4^{3(x-3)} = 4^{2x}\] \[\large \Rightarrow 3(x-3) = 2x\] \[\large \Rightarrow 3x - 9 = 2x\] do you get the process??/

Answer 2

No not really. Like how did you get "4^3(x - 3)" ?

Answer 3

\[\Large 64 = 4 \times 4 \times 4 = 4^3\]

Answer 4

so i subbed \(4^3\) into 64..got it now?

Answer 5

Okay, What is this method called?

Answer 6

which method? the whole one? or turning 64 into 4^3?

Answer 7

Yeah, I have to simplify the equation till I get x = -9?

Answer 8

The whole method for the equation.

Answer 9

careful...

3x - 9 = 2x

3x - 2x = 9

Answer 10

not negative

Answer 11

okay. so it's x = 9 ?

Answer 12

yep

Answer 13

idk the formal name of the method..but it has something to do with putting the bases the same

Answer 14

Those are called exponent rules.
If:
\[5^{6x}=5^{18x}\]
Then 6x=18x

Answer 15

exponential rules rather

Answer 16

Thanks!

Answer 17

No problem, just google them to get familiar with other rules.

Answer 18

I m with lgbasallote!:)