How many times do you need to multiply 2 by itself to get to 1024? MANY Ways to Solve!

How to solve a basic exponential equation.
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[@vanderpoolfarmsl.l.c.9983]

"MANY MATH TEACHERS WILL GET IT WRONG!!" No A+++, smiley face or bragging to friends for John. LOL!! The answer is 9

[@WRLCK777]

There are 10 2s in the equezion. But only 9 multiplycazions. So the question is wrong. My answer was 9? How many times do you need to multiply. Well the first 2 does exist on firsthand. So it does not count In the equezion.

[@debbieholoquist2059]

I hoped to see him respond to your comment. I agree with you. 2x2 is only one case of 2 multiplied by itself, even though there are two 2s.

[@jerzygutowski3170]

9

[@_Aardvark_]

The answer is 9. I think John should apply the rule of three to checking his solutions.

[@user-zx2km9ri2h]

You asked how many times to multiply not how many twos to multiply. 9

[@jerrybrickley2115]

I'm with you.

[@revolvo5519]

I don't see how the answer is 10. Theres ten 2s in the multiplication but you're only multiplying 9 times. 2x2 is one multiplication so 2x2x2x2x2x2x2x2x2x2 is 9 multiplications and the question is how many times are you multiplying 2 by itself. Not how many 2s you are multiplying!?

[@jald910]

My thoughts also. I’m positive 9 times is correct.

[@user-vo4ho3jv7z]

Poorly worded. Yes you are correct because 2^1 is not multiplying 2 times 2. However 1024 is 2^10.

[@larrywiener6327]

You get 10 times if you count the original 2, 0 but that's not what; he asked

[@israeljaimes6497]

2^9 is 512

[@user-gx1rk8yw6l]

@@israeljaimes6497 Very true. But only 9 instances of the *multiplication* occur to get to 1024.

[@billjohnson3858]

Every time I multiply 2 by itself, I get 4. No matter how many times.

[@user-gx1rk8yw6l]

This is another *beautiful* example of *not misinterpreting* the question, but showing a different & *valid* interpretation thereof. Thank you, @billjohnson3858, for this interpretation that so-beautifully shows the absence of logic in human languages! 🙂

[@terry_willis]

The formula or method needs to have a (n-1) factor because, as other have said, the first 2x2 uses two digits but is a ONE time multiplication.

[@panlomito]

1024 = 2^10 so the answer is 9 multiplications.

[@bulldog6925]

The number of times you have to multiple the digits is going to be one less than the number of digits since the first digit is a starting point; that is, there was not a math operation to create it

[@garybacchus8526]

I got 9 2 by itself once = 4 (2^2) following the pattern makes 9 times thus reaching 2^10 = 1024.

[@Geoff_G]

Once 2×2=4 Twice 2×4=8 Thrice 2×8=16 Four Times 2×16=32 Five Times 2×32=64 Six Times 2×64=128 Seven Times 2×128=256 Eight Times 2×256=512 Nine Times 2×512=1024 Edited to say John, you're wrong.

[@gnichopd]

I agree. I'm not a math teacher, but I read and understand English pretty well. 2x2 is 2 multiplied by itself ONE time. The answer to the question you asked is 9.

[@user-gx1rk8yw6l]

@@gnichopd *Very true* . The question, *as-stated* , asks for the quantity of *multiplications* . It is *not* asking for the quantity of the number '2'. This kind of question-formulation shows the absence of logic in human languages & the rather-ridiculous assumptions that said absence causes. Interesting that *most* commenters have pointed this out...

[@Briarbuddy]

Nine times

[@donavonhiss3140]

Answer is 10 guys No argument Maths is a language

[@user-gx1rk8yw6l]

@@donavonhiss3140 Yes argument. We need a useful definition of "language". If according to a truly useful definition maths is deemed a language, then in THAT language the answer is 10 and in HUMAN language the answer is 9. A commenter posted another interpretation based on human language, which leads to no numerical answer being possible.

[@billbrownster]

9 - The problem asks Not how many 2s are involved - But How many multiplications are involved. 9

[@eddiepierce7028]

9 times out of- did it in my head 2, 4, 8, 16, 32, 64, etc..

[@iamhe999]

The answer is 9 not 10, you answered a different question, what power of 2 equals 1024 that! Would be 2 to the 10th power.

[@beverleysmith8704]

I got this answer because I’d done a problem that required 2^8 yesterday. So it wasn’t a great leap. Also yesterday I questioned myself about quantities of powers and noted the difference to numbers of multiplications to try to understand it. Often stumbling around in the dark and that’s why I’m here.

[@Yup241]

"2 multiplied by itself" is 4 and that is all it will ever be no matter how many times you do it. If you add steps such as 2x4 it is no longer "2 multiplied by itself". The correct question would be, 2 raised to what power equals 1024?

[@advancedautomotivemachine4791]

Maybe the wording is confusing but I say 9. If you multiply 2 times itself one time you get 4. Two times you get 8 and so forth. It only takes nine times to get to 1024 ??

[@silverhammer7779]

Wouldn't be the first time he's used ambiguous wording for problems. The answer is 9.

[@Ayelmar]

At the title card, my answer is 9 times . 1024 is 2^10, so we multiply 2 by 2 nine more times to get to 1024. The expansion is 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.... (As I've mentioned before, powers of 2 are kind of my jam -- calculating subnet masks by day, and retro-computing by night does that for you....)

[@terry_willis]

It's actually eight more times, not nine more times.

[@danielwarren7110]

did it from binary 0000000001 = 1 and 1111111111 = 1023 so to count from 0 to 1024 you would need 11 digits 10000000000 = 1024 as each digit is double the one to the right and 11 digits in binary is the number we want but 2 which is the second digit so 10 binary digits different. meaning 2 is multplied by itself 9 times 2^10 0000000001 = 1 0000000010 = 2 0000000100 = 4 0000001000 = 8 0000010000 = 16 0000100000 = 32 0001000000 = 64 0010000000 = 128 and so on 1000000000 = 512 1111111111 = 1023 and you can do all that on the ten fingers of your hand using the ten fingers to count from 0 all fingers down to any number up to 1024 all fingers up.

[@aryusure1943]

I'm not sure I used the best method but I began to find the square root of 1024 and factored after that. 32 X 32 = 1024. Factoring both 32's I came up with 2 exponent 10 or 2 times 2 exponent 5.

[@awcampbell2002]

If this is an argument of semantics i would say that no matter how many times I try 2 times 2 is still 4.

[@silverhammer7779]

2 to the first power is 2. 2 to the second power is 4, but it is also the FIRST time that 2 is multiplied by itself. That is why the answer is 9 and not 10. Take your own advice and read the problem three times.

[@thomasraywood679]

You can only multiply 2 by itself once. After that, you're multiplying 2 by a multiple of 2 larger than 2.

[@Stephen-J-in-IA]

Computer guys know this offhand.

[@joejoe8322]

I got 9 when I did it in my head. I counted the original 2×2 as one time. Should it be counted as two times? There is only one times symbol that's why I counted it as one time.

[@russelllomando8460]

10 - basic exponents. thanks for the fun.

[@dalebruetting6177]

I agree it’s 9. I suggest Mr Math man read the problem 4 times

[@gabriellechamberlain7228]

On my calculator I pressed the multiplication sign only 9 times.

[@rodfulford4306]

Nine times, similar to sequencing where number of steps is one less than all the numbers. Its the way he tells them!

[@donavonhiss3140]

Lesson learned! Semantics, grammar, spelling, and punctuation are important elements in the language of Mathematics.

[@RodCalidge]

2^10 is indeed 1024, however, s the question is written, thenswer is 9

[@MrMousley]

Isn't 2^10 multiplying 2 by itself 9 times ?

[@quigonkenny]

9. 1024 is 2¹⁰, so you'd think the answer is 10, but keep in mind that 2² is "multiplying 2 by itself" only once.

[@Herby-1620]

If you are a computer nerd, you know the answer right away. In fact if you are any good, you know LOTS of powers of 2.

[@deograciousuwiragiye8429]

Primefactorize 1024 2power x=2 power 10 This means x=10

[@richardl6751]

For those in doubt, copy and paste this into windows calculator: 2*2*2*2*2*2*2*2*2*2= I counted very carefully and there are ten twos there. What did you get?

[@jerrybrickley2115]

How many asterisks are there? That's how many multiplications there are.

[@vanderpoolfarmsl.l.c.9983]

Someone didn't read the problem 3 times.

[@jaym8257]

x=log 1024/log 2

[@user-ee7hx1jb9x]

It should be 9 times. There are only 9 operations to get to 1024. KZbin math guy is wrong.

[@raynewport9395]

Well its about quarter past 10 now, but I think I can get to 1024 never needing to multiply anything. I'll let you know..

[@raynewport9395]

Phew. Well, there's your answer, 0.

[@user-gx1rk8yw6l]

@tabletclass BTW, at :431 you say "... will get us to 100,000 ...". Mathematically this means "< 100,000", *not* "=< 100,000". Was that "less than" what you intended the viewers to understand? Granted that from a *mathematical* viewpoint the video's question is not very difficult. But oohh... it so CLEARLY shows the *linguistic* problem! Please note also @billjohnson3858's interpretation of the question as-it-is-posed. I have also seen that you have *not* commented... If you ever wish to show the *linguistic* issues with "talking in maths", (try to) prove that both mathematically *and* linguistically "1 and 2 make 4" is absolutely True. All-in-all I wish that curriculum-designers would *quit* trying to use human language to express maths questions. Alternatively, curriculum-designers & the linguistics discipline would do well to work at improving human language so that it becomes *able* to express maths as it is *intended* . My thumbs-UP is for the *maths* view of the issue, though for the *lingual* side it should be a big thumbs-DOWN.

[@SuperVt100]

> 3

[@paulmcguire6366]

The answer to the questions asked is 9......and that is my final answer.

[@samswift4921]

10

[@FR33domLover]

Multiplying 2 by itself always results in 4. It will never produce anything else. Do it again, and you'll get 4 again. Here's what exponentiation by an integer means: First, ALWAYS START WITH 1. That's your initial "partial product." Then using the exponent as a counter, multiply the partial product by the base (2, in this case) that many (10) times. Thinking of the process this way makes it consistent---no exceptions needed. The base and exponent have a clear meaning. Thinking of it this way also explains the first and zeroth powers---they're not exceptions. The question was wrong!

[@user-gx1rk8yw6l]

Even better stated, start with the power 0 to get that initial "partial product". You are (I think) the 4th person to mention that multiplying 2 by itself always results in 4. I think (=opinion!) that IT is the NICEST interpretation-&-answer. 🙂

[@user-ri6rn7ti5h]

2^5=32 2^5=32{512+512}=1024

[@kennethwright870]

2^10=1024, so 9

[@user-ri6rn7ti5h]

2^5 =32 2^5=32

[@user-ri6rn7ti5h]

2^9=512

[@yogeshdivanaji9140]

512

[@user-ri6rn7ti5h]

2^10 =1024

[@jerrybrickley2115]

That's 10 digits, but only nine operations/ multiplications, or nine times 2 is multiplied by itself.

[@brasavid]

This teacher has a problem with english language (not only this time!). As the question is How many times you perform the action of muliplying the answer can only be 9. No discution.

[@user-gx1rk8yw6l]

You forget that multiplying 2 by itself always results in 4. Which is *yet another* interpretation of the question. So up to now *3* answers are possible--going by the comments so far. I actually disagree with the TEACHER having a language-problem. More to the point would be that stating ANY maths problem in HUMAN language is nigh-impossible to do without using ambiguous wording. So anybody *effectively* stating that 1 *specific* answer is THE 1-&-only right answer also has problems with HUMAN LANGUAGE.

[@brasavid]

You still made ONE multiplication to get 4 which is 2^2, so what is your point?

[@brasavid]

.... and when you are a teacher and you give grades to students be sure the question you put is unanbigous

[@user-gx1rk8yw6l]

@@brasavid The point is, that when taking "multiply 2 by itself" as the key phrase, what one does is this: 2 * 2 = 4 2 * 2 = 4 2 * 2 = 4 over & over again. The number of times that one does this can be infinitely large without ever getting nearer 1024 than 4. As you said in your following comment, the question must not be ambiguous. I HATE MATHS-IN-WORDS BECAUSE HUMAN LANGUAGE IS SO EFFING LOUSY!

[@deograciousuwiragiye8429]

2 power 10=1024

[@danielmadden9691]

10 times I mean

[@jerzygutowski3170]

Not enough 2 correct is 10

[@ECO473]

9

[@R4N21]

512

[@billferrol4202]

10

[@davidwynne3289]

9

[@motorbuzz4748]

9

[@atiurrahman2248]

9

[@kk6aw]

9