Italy l Very Nice Olympiad Math Exponential Problem l find value of x?

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[@domosautomotive1929]

I'm glad you explained that 1= -1+2, I would have never figured that out

[@tinashechipomho]

That kind of detail is excruciating,😮

[@ELW-x8d]

Maybe this video is rather a support for beginners? In this case, I think that the person wanted to explain the decomposition of the powers to find out "common factors" ...

[@SanePerson1]

17 minutes? For all intents and purposes, it was finished at the 3 minute mark: 8^(x - 1) = 48 or dividing both sides by 8, 8^(x - 2) = 6. Since 8 = 2³, 2^(3x - 6) = 2 × 3. Dividing both sides by 2 again, 2^(3x - 7) = 3. Take logs of both sides ⇒ (3x - 7)log2 = log3, which can be simplified to x =( (log3/log2) +7 )/3. If you've memorized a few base-10 logs, log2 = 0.301, log3 = 0.477 and you're done. All the extraneous manipulations of logarithms is a waste of time.

[@maadhavrkmark5474]

You're right ✅️

[@noski33]

Agree

[@fraffra97]

Yes but, I mean, monetization...

[@mrray9946]

Que relajante

[@Harriawolff]

3 min in mind

[@stevesilva2780]

8^(x+1) - 8^(x-1) = 3024 8*8^x - (8^x)/8 = 3024 [(8^2)*(8^x) - 8^x]/8 = 3024 8^2 * 8^x - 8^x = 8* 3024 8^x 8*(8^2 - 1) = 8* 3024 8^x = (8*3024)/63 8^x = 384 X = log384/log8

[@garryfrancois2320]

Good job bro!

[@riccardogrossi1770]

8^x *8 - 8^x/8 = 16*3*63 8^x = 384

[@johnmaynor3851]

It’s was a good refresher for me.

[@luiscarloscamargo9941]

Sensacional !!!

[@donotelly]

I generally don’t reduce further once I get to a logA/logB equation. Let the calculator do its job.

[@EthanHolder0]

I don't know why people think turning succinct logs into a bunch of fractions that still have logs in them is simpler. Why introduce potential arithmetic errors in "simplifying" a log, when the calculator does not care at all and works just as well either way.

[@jacobcombs1106]

I don't know why but your way feels like it takes longer to me. Here is how I solved it. 8^x×8-8^x/8=3024 8^x(8-1/8)=3024 8^x(63/8)=3024 8^x=3024×8/63 8^x=384 ln(8^x)=ln(384) x×ln(8)=ln(384) x=ln(384)/ln(8) x=~2.86

[@rumpeldrump]

Mathematics is not the same as arithmetic.

[@jacobcombs1106]

@rumpeldrump the same way squares aren't the same as polygons. All squares are polygons but not all polygons are squares. All arithmetic is mathematics but not all mathematics is arithmetic.

[@rumpeldrump]

@@jacobcombs1106 I don't see it that way. sqrt(2) is precise, 1.4142 is not 17/12 either.

[@jacobcombs1106]

@@rumpeldrump Everyone knows it's a blueberry because oranges don't have doors. What does any of that have to do with definitions? Yes describing irrational numbers like the square root of 2 with the √ is more precise than the decimal form, that has absolutely nothing to do with the definition of mathematics or arithmetic? Mathematics is defined as: the abstract science of number, quantity, and space. Arithmetic is defined as: the branch of mathematics dealing with the properties and manipulation of numbers. Arithmetic is a kind of maths.

[@rumpeldrump]

@jacobcombs1106 you talk a lot and say nothing, yes and arithmetic is a sub-area but not precise. everything you say is nonsense.

[@stpat7614]

No fractions in this solution: 8^(x+1) - 8^(x-1) = 3024 8^(x-1+2) - 8^(x-1) = 3024 8^(x-1)*8^2 - 8^(x-1) = 3024 8^(x-1)*64 - 8^(x-1)*1 = 3024 8^(x-1)*(64 - 1) = 3024 8^(x-1)*63 = 3024 8^(x-1)*63/63 = 3024/63 8^(x-1) = 48 log(8^[x-1]) = log(48) (x-1)*log(8) = log(48) (x-1)*log(8) = log(6*8) (x-1)*log(8) = log(6) + log(8) (x-1)*log(8)/log(8) = (log[6] + log[8]) / log(8) x - 1 = log(6)/log(8) + log(8)/log(8) x - 1 = log_8(6) + 1 x - 1 + 1 = log_8(6) + 1 + 1 x = log_8(6) + 2

[@RafayKhan-h6q]

😮😮 good

[@borisjeud8464]

X= 2.86...

[@md.mominshahriar]

Dude explained how 2×2×2=8, but didn't show how he got 48 from dividing 3024 by 63

[@anlag2]

In this case movie will be more than hour

[@patricaramello]

63=3·3·7 3024/3=1008 1008/3=336 336/7=48 You can use a calculator too 😅

[@md.mominshahriar]

@@patricaramello I know how to do it. I'm just checking the channel's sanity

[@laurasaenz3021]

8^(x+1) - 8^(x-1) = 3024 8^x*(8-1/8) = 3024 8^x*(63/8) = 3024 8^x*(3^2*7/2^3) = 2^4*3^3*7 8^x = 2^7*3 (2^3)^ x= 2^7*3 2^(3x) =2^7*3 2^(3x-7) = 3 3x-7 = log_2(3) x = (7 +log_2(3))/3

[@nucki222]

X = ln 384 / ln 8 ; X = 2,86

[@tcmxiyw]

Put off multiplying small factors to get a large number that you’re only going to factor later. Smaller factors are easier to work with.

[@cyruschang1904]

y = 8^x 8y - y/8 = 3024 = 8(3)(2)(63) 63y = 8(8)(3)(2)(63) y = 8(8)(3)(2) = 3(2^7) = 8^x = 2^(3x) 2^(3x - 7) = 3 3x - 7 = (log3)/(log2) x = 7/3 + (log3)/(3log2)

[@YmohTheFrog]

How does it take 17 minutes to do 8^x(8-1/8), divide both sides by (8-1/8) and do a log operation??

[@MrAlvaroxz]

17 mins!!! Common factor 8^x then u are done... 8^x(8-1/8)=3024 8^x=3024/(63/8) 8^x=3024*8/63 x=log_8(3024*8/63)

[@z-ryk]

8^(x+1) - 8^(x-1) = 3024 => 8^x * 8 - 8^x * (1/8) = 3024 => 8^x (8 - 1/8) = 3024 => 8^x (63/8) = 3024 => 8^x = 3024/(63/8) => 8^x = (3024 * 8) / 63 => 8^x = (3024/9 * 8) / 7 => 8^x = (1008/3 * 8) / 7 => 8^x = (336/7) * 8 => 8^x = 48 * 8 => 8^x = 6 * 8 * 8 => 8^(x-2) = 6 => (x-2).ln(8) = ln(6) => x-2 = ln(6)/ln(8) => x = log_8(6) + 2

[@THyperon]

Everybody has a calculator... so at stage x-1=log48/log8 --> x=1+log48/log8 = 1+1.862 = 2.862 ✅️

[@rumpeldrump]

Very imprecise.

[@Victurf]

Avec cette manie de changer de base, on ne sait toujours pas que vaut la réponse !

[@stevenjeng1237]

I find that you are always doing complex way.

[@craigeverhart4755]

Every step explained

[@lanegibson6859]

That is not how to properly write an 8.

[@wiseview1444]

trivial

[@kagan1429]

This is not an Olympiad question. Don’t waste people’s time with such simple questions and unnecessarily long solutions!

[@davidreid7293]

Mathematical manoeuvring but what is the purpose?

[@MrAboy97]

B/s 😂

[@tonir299]

8^(x+1) - 8^(x-1) = 3024 || *8 8^(x+2) - 8^x = 3024*8 (8^x)*(8^2 - 1) = 3024*8 || ÷63 8^x = 48*8 || factorize 2^(3*x) = 2^7*3 || log 3*x*log2 = 7*log2 + log3 || ÷log2 3*x = 7 + log3 / log2 || ÷3 and change log base to 2 x = (7 + log[2]3) / 3

[@SamsonMohamed]

Excellent teacher! Thank you!!!

[@Trog1959]

I'm horrified that this is (supposedly) a math Olympiad question

[@BossDropbear]

I very much doubt it to be Olympiad standard, its a slightly dressed up log question, 4th form/yr10 roughly, maybe 1 grade higher if I am generous.

[@prosperchibharo957]

Maths olympiad and someone is winding and unnecessarily long

[@maxm9703]

waste of time

[@jimmygarcia9698]

Dude couldn't 😢

[@NoobVSProlegendary]

Can’t you just make the bases of 8 the same and the power is like 378 so x + 1 x - 1 is equal to 8 to the power of 378

[@afzalabubakr2298]

You are doing baby sitting.Some of every second step unnecessary.Boring