What is the solution to the equation 64^(4-x)=4^(2x)? They want me to use complete sentences explaining how I did this so could you give me the steps on how to solve it? It has to be in approximate decimal form.

Question

shadowlegendx. · Answer

hi

anonymous · Answer

hey. you wanna solve? lol. because I can't.

shadowlegendx. · Answer

What grade are you?

anonymous · Answer

11th

shadowlegendx. · Answer

I thought you were 19...

anonymous · Answer

it's a real long story, man. I had to drop out because of family and now im taking it online.

shadowlegendx. · Answer

oh....sorry for bringing it up >.>

anonymous · Answer

nah it's okay. you aren't gonna solve, are you?

shadowlegendx. · Answer

Whats the ^ mean?

shadowlegendx. · Answer

Powers?

anonymous · Answer

yeah, it's an exponent.

anonymous · Answer

I know more than you :3 that's sad... lol

shadowlegendx. · Answer

I technically already knew what it was...I was just making sure ;)

anonymous · Answer

oh okay, then by all means, proceed

shadowlegendx. · Answer

Idk...usually being called a turd doesnt inspire one to do work for ya ;)

anonymous · Answer

you don't even know how to do it, do you? lmao

shadowlegendx. · Answer

I probably do...somewhere in my head...but you should probably ask someone who hasnt been up for over a day ;)

anonymous · Answer

well I asked and you were the only who replied soo... lol. I took the ACT today so I have no more brain left for more math D:

shadowlegendx. · Answer

Get some rest then :)

anonymous · Answer

Psshh I wish. I just have this one assignment left and im trying to get it done

shadowlegendx. · Answer

Is it a " last minute " one ;P

anonymous · Answer

:/ yes. -____________-

shadowlegendx. · Answer

Welcome to the Club

ranga · Answer

64 = 4 x 4 x 4 = 4^3
Replace 64 with 4^3.  Simplify.  Since the bases are the same on both sides of the equation, the exponents must be the same.  Equate the exponents and solve for x.

shadowlegendx. · Answer

Wow...nice was of putting it ranga

anonymous · Answer

Thank you, ranga, for helping me on this :) I appreciate it!

shadowlegendx. · Answer

You greens know your stuff :)

ranga · Answer

Thank you @ShadowLegendX. 

You are wleocme @megangray32.

ranga · Answer

$$\Large 64^{4-x} = 4^{2x}$$$$\Large (4^{3})^{4-x} = 4^{2x}$$$$\Large 4^{12 - 3x} = 4^{2x}$$Bases are the same.  Therefore, exponents must be the same.  $$\Large 12 - 3x = 2x$$Solve for x.

anonymous · Answer

12/5, right?

ranga · Answer

Yes, but they want the answer in decimal.

anonymous · Answer

oh yeah, it'd be 2.4 then?

ranga · Answer

Yes.

anonymous · Answer

okay thank you again

ranga · Answer

Glad to be able to help.

adrynicoleb · Answer

*walks through question* Don't mind me, just stalking lalala~