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

Question

lgbasallote · Answer

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

anonymous · Answer

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

lgbasallote · Answer

$$\Large 64 = 4 \times 4 \times 4 = 4^3$$

lgbasallote · Answer

so i subbed $4^3$ into 64..got it now?

anonymous · Answer

Okay, What is this method called?

lgbasallote · Answer

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

anonymous · Answer

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

anonymous · Answer

The whole method for the equation.

lgbasallote · Answer

careful... 

3x - 9 = 2x

3x - 2x = 9

lgbasallote · Answer

not negative

anonymous · Answer

okay. so it's x = 9 ?

lgbasallote · Answer

yep

lgbasallote · Answer

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

anonymous · Answer

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

anonymous · Answer

exponential rules rather

anonymous · Answer

Thanks!

anonymous · Answer

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

theviper · Answer

I m with lgbasallote!:)