Solve the exponential equation:
4^4x-2=1/32
=2^8x-4 = 2^8x2^-4

Question

Solve the exponential equation:
4^4x-2=1/32
=2^8x-4 = 2^8x2^-4 <--- why 2^8x2^-4?

anonymous · Answer

your job is to see that 
$$2^2=4$$ and also that 
$$2^{-5}=\frac{1}{32}$$ so you can write both of these with the same base

anonymous · Answer

ok, but why on my solutions is it listed as $$2^{8x}2^{-4}$$ I guess i fail to see where they get the 2nd 2 from

anonymous · Answer

I mean as a step in the problem

anonymous · Answer

and therefore 
$$4^{4x-2}=(2^2)^{4x-2}=2^{8x-4}$$ making 
$$2^{8x-4}=2^{-5}$$ and so 
$$8x-4=-5$$

anonymous · Answer

thus x = -1/8

anonymous · Answer

yes. i made a typo as well

anonymous · Answer

Okay, thanks, I was only trying to understand my professor's solution key.. I did not understand her step... but apparently it is not needed.

anonymous · Answer

oh no, what i wrote is right

anonymous · Answer

well it is true that 
$$2^{8x-4}=2^{8x}\times 2^{-4}$$ but i am not sure why that helps your cause

anonymous · Answer

Ahh I see now that you type it like that!  I look too deep sometimes.  I guess she wants us to understand all steps.. but most of the time it confuses me

anonymous · Answer

$$2^{8x}=2^{-5}\times 2^{4}=2^{-1}$$ so 
$$8x=-1$$ seems like way unnecessary work to me. you already know 
$$8x-4=-5$$ why not just solve that?

anonymous · Answer

I agree.  Wish I could have this program running during our quizzes

anonymous · Answer

and you know, how you have it typed up there.. that is exactly how she has it typed.