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# when y = 2^x, write 4^x in terms of y

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1. I can't seem to comprehend this.

If y = 2^x, then 4^x will surely by 2*y, to get 2 * 2^x = 4^x.

Yet the answer seems to be y^2. Why is that? Wouldn't 2^x * 2^x = 4^2x, not 4^x ?
2. (Original post by frostyy)
I can't seem to comprehend this.

If y = 2^x, then 4^x will surely by 2*y, to get 2 * 2^x = 4^x.

Yet the answer seems to be y^2. Why is that? Wouldn't 2^x * 2^x = 4^2x, not 4^x ?
You seem to think that . That is not true. Instead, we have . Check it with your calculator.

In general: . This obeys the indices law (note that the bases have to be the same).

However, . So .
3. (Original post by frostyy)
I can't seem to comprehend this.

If y = 2^x, then 4^x will surely by 2*y, to get 2 * 2^x = 4^x.

Yet the answer seems to be y^2. Why is that? Wouldn't 2^x * 2^x = 4^2x, not 4^x ?
You are getting your rules of indices wrong.

When we multiply, we add the indices. e.g.

When we raise to a power, we multiply the indices, e.g.

Hence returning to your example, which is not the same as 4^x
Meanwhile,

Edit: Too slow...
Second edit: And a LaTeX error...
4. when you multiply you add the powers so,

Multiply when a power is raised to another power
5. (Original post by frostyy)
...
If it helps, you may want to think of as

So if you multiply it by 2: .

That's the way I teach it to my students.
6. (Original post by Zacken)
If it helps, you may want to think of as

So if you multiply it by 2: .

That's the way I teach it to my students.
Okay, thank you, I understand why I was wrong in the first place.

Yet I still fail to get this:

Surely, it'd be 2^x + x, according to the rules of indices?
how is 2^x * 2^x = 4^x? Does this mean that 4^x is the same as 2^2x?
7. (Original post by frostyy)
...
Indeed, it does. Have you heard of the rule that .

So .
8. (Original post by Zacken)
Indeed, it does. Have you heard of the rule that .

So .
Thank you. I never expected a 1 marker to show me this many holes in my logic and knowledge (perhaps intelligence too as of being unable to see the links ;p).

Cheers
9. (Original post by frostyy)
Thank you. I never expected a 1 marker to show me this many holes in my logic and knowledge (perhaps intelligence too as of being unable to see the links ;p).

Cheers
It's good that it has, now you know that you can work on them. It might be useful googling "indices laws" and refreshing your memory.
10. (Original post by Zacken)
If it helps, you may want to think of as

So if you multiply it by 2: .

That's the way I teach it to my students.
You're a teacher?
11. (Original post by Serine Soul)
You're a teacher?
I tutor a bunch of year 9's thrice a week, helps stave off the boredom that sets in when you don't go to school.
12. (Original post by Zacken)
I tutor a bunch of year 9's thrice a week, helps stave off the boredom that sets in when you don't go to school.
Ah I see

Do you give them stickers if they're good?
13. (Original post by Serine Soul)
Ah I see

Do you give them stickers if they're good?
That's a fantastic idea, I wonder if that's what Cambz supervisors do.
14. (Original post by Serine Soul)
Ah I see

Do you give them stickers if they're good?
I bet he gives them lashes with his cane
15. (Original post by Student403)
I bet he gives them lashes with his cane
16. (Original post by Zacken)
PRSOM
17. (Original post by Zacken)
That's a fantastic idea, I wonder if that's what Cambz supervisors do.
With only the finest

(Original post by Student403)
I bet he gives them lashes with his cane
Not. *whack* STEP. *whack* Standard. *whack*
18. (Original post by Serine Soul)
With only the finest

Not. *whack* STEP. *whack* Standard. *whack*
XD
19. (Original post by Zacken)
That's a fantastic idea, I wonder if that's what Cambz supervisors do.
In my experience, they just didn't glare at you if you got something right.
20. (Original post by Gregorius)
In my experience, they just didn't glare at you if you get something right.
Can't wait to not be glared at, sounds like a real treat.

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