Question

Another giving another medal before I leave...

4^1+2x=1024

Answer 1

x=510

Answer 2

it's 4 to the 1+2x power equals 1024

Answer 3

akshay how did you get 510?

Answer 4

\[4^{1+2x}=1024\]

Answer 5

right if

Answer 6

@akshay1234 solved other equation

Answer 7

Please double-check that you've copied this problem correctly. It's highly unusual to see 4^1. Use parentheses to group that 1 with that 2x, or, better yet, use Equation Editor (as you just have). @Opulentgal: Please now try solving this equation for x, showing your work.

Answer 8

I asked the teacher what it was and she said 4 to the 1+2x power equals 1024

Answer 9

First of all right 1024 as 2^10
Second of all right :\[4^{1+2x}=2^{2^{1+2x}}=2^{2+4x}\]

Answer 10

I believe that's the correct interpretation. I'm curious how you'll approach the solution. What would you do first?

Answer 11

I need to know how to express exponents when I type...

Answer 12

well mm, I would try to solve for x?

Answer 13

after this notation your equation looks like:
\[2^{10}=2^{2+4x}\]

Answer 14

That's a separate question, and a good one....but please let's solve \[4^{1+2x}=1024\] first.

Based upon the hints given you above, can you now solve for x, @opulentgal?

Answer 15

express the left side as a log to bring down the exponent?

Answer 16

@ifrimpanainte: Thanks for your very appropriate guidance.

Answer 17

If is good! :)

Answer 18

\[2^{10}=2^{2+4x}\]

Answer 19

is correct (and yes, "good").
Hint: How would you now simplify \[2^{10}=2^{2+4x}\]???

Answer 20

cut 4 both side

Answer 21

@akshay1234: Thanks, but would you please let Opulentgal try to find her own solution?

Answer 22

1+2x=4 remain

Answer 23

Wrong tag.
Anyway, @akshay1234
\[\Large 4^4\] has no part in this :P

Answer 24

not getting it because since I am methodical, I need step by step; working on this end...

Answer 25

You mentioned logs @Opulentgal
Are you more comfortable with those?

Answer 26

@akshay1234 Thank you for that correction.
Now, before jumping right into it, first, try to understand what method works for the asker in question here ^_^

Answer 27

you got 1+2x=5 then send 1 right side

Answer 28

Virtrual <shush>
@akshay1234
no spoilers ^_^

Answer 29

2x=4 comes up then x=4/2

Answer 30

i need to get the 1024 to match the base on the left side so exponents be =
one to one

Answer 31

<sigh>

Answer 32

x=2

Answer 33

Okay, that's a good way to do it too, @Opulentgal
Can you express 1024 as 4 raised to some exponent?

Answer 34

you can cheak by puting x value in your question ok

Answer 35

@akshay1234 Would you PLEASE let Opulentgal do her work herself? On OpenStudy we do NOT do other people's work for them nor give them the answers outright. Stop now, please.

Answer 36

I'm sorry, @Opulentgal
For two things, firstly, this mix-up concerning akshay

And second, there isn't really any methodical way to get what exponent you need to raise 4 to so that you get 1024...

Even if you use logs, you still have to know for a fact that 1024 is in fact, 4 raised to...what? ^_^

Answer 37

Assuming that \[2^{10}=2^{2+4x}\] is correct, please note, Opulentgal, that the 2 sides have the same base. Is there a way to eliminate that common base?

Answer 38

^Or work from there. lol :)

Answer 39

well mm, you could bring down the exponents since the bases are the same..right

Answer 40

Sometimes, wording is crucial, especially when you're explaining your work.

Since the bases are equal, their exponents must also be equal
^is the sound reasoning for this.

So, your next step should be...?

Answer 41

"well mm, you could bring down the exponents since the bases are the same..right?" Yes! "Since the bases are equal, their exponents must also be equal."

Answer 42

10=2+4x
10-2=2+4x-2
8=4x
8/4=4x/4
2=x

Answer 43

Bravo.
^_^

Answer 44

thanks mm and terenz, I must give a medal but to whom, wish I could give to both of you...

Answer 45

Really, really cool, Opulentgal!! Please take notes on this conversation, so that you'll have something helpful to refer to later on.

Answer 46

Don't worry about medals. It's enough that you learned ^_^

Answer 47

Give terenzreignz the medal and reward me by continuing the positive involvement you've shown here!

Answer 48

Way ahead of you. As usual, a pleasure working with you, professor :)
^_^

Answer 49

mm,. I pay it forward by answering history questions since I like history! :)

Answer 50

Great idea!!!