Question

How would you solve this equation: 64^x=4^x+4 (the +4 is with the x, the exponent over the 4 is x+4)

Answer 1

\[64^{x} = 4^{x+4}\] <--- like that?

Answer 2

Yes, like that.

Answer 3

okay so thing of how u can simplify 64 how many times does 4 go into 16?

Answer 4

* 64

Answer 5

It goes into it 16 times. What I have so far is \[4^{3+x}=4^{x+4}\]

Answer 6

did u get it? Do you want me to walk u through it or do you want me to just post the steps

Answer 7

Walk me through it would be the best way.

Answer 8

PERFECT since the bases are the same, you cancel them out and it becomes
3+x = x+4

Answer 9

Yeah, I got that.

Answer 10

Now it's simple algebra.. do you know what to do now, or do you want me to continue?

Answer 11

Continue please, so that I don't mess up.

Answer 12

so now you have to get the xes to 1 side and the numbers to the otherside

so...
4-3= 1
x-x =0
0, thus there is No solution.....
to check :

http://www.wolframalpha.com/input/?i=64%5Ex%3D4%5Ex%2B4

Answer 13

(4^3)^x=4^(x+4)
4^(3x)=4^(x+4)
3x=x+4
2x=4
x=2

Answer 14

You added +4 to 4^x, it's actaully \[4^{x+4}\] not \[4^{x}+4\]

Answer 15

ohhhh wait hold up

Answer 16

\[4^{3x}=4^{x+4}\]

Answer 17

that's where ur wrong you did 3+x in stead of 3x

Answer 18

When I tried it, I got x=1. These are the steps I did: \[4^{3}=4^{x+4}\]
\[3^{x}=x+4\]
\[2x=4\]
x=2

Answer 19

so the real answer is ...
3x=x+4
3x-x= 2x
2x=4
divide by 2
x=2

Answer 20

Yes, we were both wrong at certain points. Thanks.

Answer 21

lol ur welcome