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[@jimmywatson7950]

Sir, In the equation 4ˣ=x⁶⁴, both 4ˣ and x⁶⁴ are continuous function if x=1, then 4¹>1⁶⁴ if x=2, then 4²

[@sandippatwari927]

By bisection method

[@AbhinabRay-tf5gh]

Vaah sir kya logic hain. Love you very much sir❤❤❤❤

[@ABCDEFGH4567-8]

Set f(x)=4ˣ-x⁶⁴ Clearly x=256 is solution. f(0)=1>0 f(1)=3>0 f(2)

[@Qwert-c1]

😂

[@kx_lovestatus7175]

😂😂 baag aya se

[@arkodasgupta0412]

@@kx_lovestatus7175 why laughing bro? Jo roots non solvable hote ha manually, computers use this algorithm for root finding. This is a very basic one. There are other ones such as newton raphson which converge much faster

[@pecchewaleshukla]

@@arkodasgupta0412 bhaiuya newton rapshon method kab padhaya jata hai i mean iit ke syll. me hai ??

[@ABCDEFGH4567-8]

@@arkodasgupta0412 pata nahi hoga usko... isliye has raha hai.... Numerical analysis/ methods naam ka koi branch hai mathematics ka sayad nahi pata hoga..may be that's why he is laughing

[@SantoshChoudhary-vz5yg]

We could use log here and Equation that we get is By taking log base 2 on both side x=32log(x) x=16*logx² We can now analyse the equation and get that X must be greater than 1 Try to make the equation symmetrical by putting logx²=16 Hence we get x=2⁸ We can now varify our solution 2⁸=2⁴x2⁴ Hence x=256

[@kushagramishra1729]

lekin sir 256 ke alawa 2 aur solutions hai iske ek -1 se 0 ke beech me aur ek 1 se 2 ke beech me

[@aryankushwaha7028]

Yes i also think so that's why I analyze behaviour , after I plot the graph on desmos then i got to the point

[@kushagramishra1729]

@@aryankushwaha7028 There are totally 3 real solutions. One of them is 256

[@ABCDEFGH4567-8]

​@@kushagramishra1729 Use the numerical analysis to find the other 2 solutions. Apply the bisection method

[@Aadi_375]

X = -1,0 rakhe to equation satisfy bhi to nahi ho raha hai

[@Sudhanshuranjan2809]

​@@Aadi_375 bhai wo -1 ,0 ko solution nhi bol rha, wo bol raha(-1,0) k beech me ek solution hai aur (1,2) k beech

[@vishalachakravarthy2082]

Very much impressed sir . thank you for this knowledge sir lots of respect to you sir

[@shlokthosar8094]

Sir please start any series for Olympiads

[@ankeshiitkanpur2008]

Can anyone please explain me the first step how sir have written 4= x^64/x

[@Beliver_of_unseen]

Taking 64th root

[@ankeshiitkanpur2008]

@@Beliver_of_unseen ok thanks 👍

[@alankritgaming8254]

Can we solve it by taking log both sides ❤

[@rudrakshthaokar9789]

Yes

[@samyakwagde4522]

Aap accha samjhate hain❤❤❤🎉

[@Goodbro0007]

Sir graph se answer alag aarahe hai

[@notstorm]

sir rough graph se to ham directly bol sakte hai 3 solutions honge, usme se ek x = 256 pe aayega?

[@Aslian_Harsh_momentum4.0]

Sir class 11th batch KZbin par digiye please nahi to aap par 500💵me class dijiye

[@PiyushKumaryadav-yd5ft]

4^x =x⁶⁴ 4 = log base(x) arg (x⁶⁴) Now 4=64log(base x) arg(x) Then 4 = 64 😮😮😮😮😮 So equation is wrong because it is not possible

[@AKASHJEEASPIRANT26]

Log ka base x Lia hai to Xlog4(base x) = 64 hoga idiot

[@Jawahirullah-u2b]

Sir function ki playlist gyab hoagye sir And ap ki 10 initial video bhi nahy hy sir And 1 to 11 nahy hy 12 to 17 hyy We are 2waiting please sir re uploaded

[@Oppositeofmyprofilephoto]

can we solve this with Logarithm?

[@kunjdubey2982]

Abe galat h 1.02 and -.9 hoga

[@crazymathematician88]

Take log both side of base 4 done in minf

[@zeroplays9915]

then what youll have to use Lambert W function which is not in jee syllabus

[@crazymathematician88]

@@zeroplays9915 what Is lambert w function? Can you explain me

[@MrinalThakur-xi9tm]

Sir this was quite good problem

[@Artist_Entertainment_Art]

Sir isko log ke rule ka use karke solve kr skte h

[@NDA_Success_Tips]

Sir apke channel per video hide हो gai है 😢

[@railwaymathsspecial]

मैं तो orally solve कर दिया कुछ ढंग का question लाओ

[@SKtotalPremium]

What is x is zero? 😅

[@Debarghya_]

It has three real solutions as per Wolfram alpha

[@sentishiva29878]

Here are the two solution which one is 256 And one between (1and 2) real solution

[@rachitbajaj5301]

Idhar log kyu nhi le sakte?

[@spaceodyssey9788]

X must be greater than 0. It's not given here. I think that may be the reason

[@ayushsingh-f1t8z]

yes

[@uniquearijitian8387]

sir maine log se nikala lekin aapke tarike se bhut jaldi ban gya kyuki main jaldi guesss nhi kar pata

[@ABCDEFGH4567-8]

4ˣ=x⁶⁴ Taking both side log xln4=64lnx ln4/64=lnx/x lnx/x=ln2/32 (1/x)ln(1/x)=(-1/32)ln2 Taking both side W-lambart function. W[(1/x)ln(1/x)]=W[(-1/32)ln2] ln(1/x)=W((-1/32)ln2) 1/x=e⁻ʷ⁽⁽⁻¹/³²⁾ˡⁿ²⁾ x=eʷ⁽⁽¹/³²⁾ˡⁿ²⁾ x=1.02 x=-0.97 x=256

[@MaheshKumar-lx1ku]

Ye function Kab padhaya jata hai??

[@snowball1002]

​@@MaheshKumar-lx1ku not in jee syllabus

[@shivx3295]

Lambard W function ke baare mai kaha se seekha?

[@tmrapper6378]

​@@shivx3295professor Newton's

[@MaheshKumar-lx1ku]

@@snowball1002 ohhh...

[@Study77-lr3xm]

Maine ise log leke solve kar diya

[@INFORMATIONKNOWLEDGE.]

Log krke ho skta 😮

[@studying3628]

Sir aapne pw kyon chora , please reply 👏

[@aditigulve6471]

sir log leke ans aa gaya tha.........

[@Salim_Subzar]

POV : You are a Coder 💀 x ≈ 1.0223929402057803 x ≈ -0.9790169349577846

[@hsingh8625]

Log lelete aasan padhta

[@pranaykumar5683]

❤❤❤❤❤❤❤❤❤

[@SubrataChattaraj-e8y]

256.

[@thotakoushik]

Hi

[@Prathamesh_Laddhad]

I ATTEMPTED WITHOUT SEEIGN SOLUTION MY ANS IS 256

[@investmentwithsachin1]

I

[@JoaoPedro-js6mk]

Hame to sir ne ye Kara dia tha wo sare coaching teachers ke association me h maths ke islie unhe daravne question milte rehte h or hme dete h taki hmari aukat pata chale...

[@dheeraj76]

Sir please upload old videos of class 11 and 12.😢😢😢😢😢

[@ManishKoiri-qw3xm]

By taking log both sides directly

[@zeroplays9915]

then what youll have to use Lambert W function which is not in jee syllabus

[@NutanSingh-vx4we]

Yes i have also done by this method

[@ridul]

Every Olympiad students know these questions 😂😂😂😂

[@rajshauryz]

Maine log leke hit and trial se kardiya (X)^(32/x)=2

[@veydantliit8952]

Bhai tere auto correct ne teri sacchai dikha di😂

[@Idk2007-fx4cs]

​@@veydantliit8952pehele kya tha

[@zeroplays9915]

then what you'll have to use Lambert W function which is not in jee syllabus

[@taseen5945]

sir , i was the type of student to think to bring log in first attemp, such a beautiful way to solve

[@aarjav4138]

I Actually Solved It Using Basic Log Only🤷‍♂️

[@anirudhsingh1623]

Can you share the solution plz 🙏🏻

[@zeroplays9915]

@@aarjav4138 then what youll have to use Lambert W function which is not in jee syllabus

[@uncannyroaches5933]

xlog4= 64 logx logx/x= (log 4)/64 logx/x= (4log4)/256 logx/x= log 256/256. easy peasy x= 256

[@housewiring1136]

X=2 ka power 1/32 hoga

[@warsiboymotkee9789]

Sir ye log se nhi ho sakta kya

[@motivationmastery5442]

Yai question graph se ho sakta hai kya ?

[@Idk2007-fx4cs]

Use graph to find number of solutions

[@AdityaK10-A]

why can't log be used sir?

[@zeroplays9915]

then what youll have to use Lambert W function which is not in jee syllabus

[@NileshArt916]

Sir 11 ki kuch playlist nhi mil rahi hai kya karu? Help

[@rahulmahato4072]

4^x =x⁶⁴ xlog4=64logx 1/64 log4=1/x logx 4/256 log4=1/x logx 1/256 log4⁴ =1/xlogx x=256😊

[@sangeeta3729]

good one

[@marrythebun-bun2501]

This is what I did as a neet student 😂

[@rahulmahato4072]

@marrythebun-bun2501 whats wrong with this???

[@harshpandey8528]

Not defined because a≠0 a>0

[@NamanAggarwal87363]

2nd solution 4*x = 4* 64log x at base 4 ||. x =64 log x at base 4 x/64 = logx at base 4 Now by hit and trial x =256 satisfies

[@tdstudymotivation]

Aap basic mathematics ki videos bna do sir

[@Sugar-wx8qt]

I will suggest you to revise calculus😂😂 cause the graph will provide you 3 unique solutions for this equation..

[@sandeepchakrwarti2468]

Thoda details mai kiya karo sir ji..ye divide mai kaise aaya

[@NaveenTanwar-l2f]

Vha god of mathematics❤

[@ShadowGaming-qf6tf]

BY COMPARING POWER X=64

[@NutanSingh-vx4we]

256 by taking log both sides

[@ipshitpaul]

X=32log2(x) X=256 satisfies this equation... Let's assume f(x) =x-32log2(x) F`(x) =1-32/x.log2... This is clearly decreasing in the interval (256, infinity)

[@zeroplays9915]

how did you guess x=256 either youre a genius or a cheater then

[@joshiukdb]

I was drawing graph and thought that there are two solutions but suddenly remembered that an exponential function has positive base always, so those who say that there are two solutions are wrong...

[@KotavlogsJEEaspirants-rt2ru]

Bro Ur right but in this case base x is in power of even no. 64 , so it does not matter wether no. is postive or negative.....

[@joshiukdb]

​@@KotavlogsJEEaspirants-rt2ruyou didn't understand Actually for exponential functions base is always positive and not equal to one. i.e. domain of x⁶⁴ is x€(0,oo)-{1} Reason: If base is 0 or 1 then function will become a constant function. If base is negative then it may give false roots. For ex x^(1/2) gives unreal roots for negative x. Hope you got it.

[@joshiukdb]

​@@KotavlogsJEEaspirants-rt2ruthis is important rule. Even q in adv use this rule.

[@n10jaiswal]

In Very short 4*64=264😅😅😅

[@Sam.69.]

X= 1/64

[@SohamGhosh-xu9qk]

Did by graph 4^x is increasing function wheres x^64 is decreasing so it meets at one point 0,256

[@Vr24j]

Did u used any website to draw these graphs 🧐🤔

[@SohamGhosh-xu9qk]

@@Vr24j Use desmos

[@PiyushKanswal3769]

Aap bahut acha samajhate ho

[@Renu.Pahadi]

Sir your batch is awesome

[@JayniMiteshPatel]

whyy cant v take log

[@SANJEEV-po3im]

Sir kya aap engineering math's ki new series start karwa sakte ho kya .apka samajh aata hai bus .😊

[@Love_seeker-143]

Sir iss question 3rd step tak toh maine bana liya tha but uske baad jo apne divide and multiply kiya hai woh mai nahi soch paya 😢. Apne ye thought kaise arise kiya aur 4 se kyu aur kaise apne predict Kiya pls tell sir.

[@CatalpaGG]

Approach questions seh hi build hoti h

[@Love_seeker-143]

@@CatalpaGG woh mujhe pata hai but ye approach jo ki comparison ka hai maine bhi lagya tha but 4 sir ne jo 4 step mein divide multiply kiya hai woh literally critical thought tha.

[@zavierbanerjee5171]

You may ask this question : what number we can multiply with 64 and also raise it to power of 4 will give us the same number? Like 64*4 = 256 and (4)^4 = 256! This is because, in the equation, we want to bring it the x^(1/x) format... So, in the LHS, i.e, 4^(1/64), we multiply and divide by 4, so now the LHS => 4^(4/64*4) this is same as => (4^4)^(1/256) => 256^(1/256) !

[@rajjaiswal2379]

Question easy hai

[@shubh2s305]

Sir i did it by taking log on both side

[@Blue_Nades]

Lambert w

[@Takhatsinghcharan-ge2wn]

Taking log both side to the base 2 ,we get X=32 log X base 2 Now log X base 2= k So X = 2^k Put 2^k= 32 k 2^(k-5)=k Clearly k= 8 So X=2^k=2^8=256

[@SamyakMeshram1]

Sir, please 😟 make a video on the question : Q. The equation (x ^ 2 + x + 1) ^ 2 + 1 = (x ^ 2 + x + 1)(x ^ 2 - x - 5) for x \in (- 2, 3) will have number of solutions, (1) 1. (2) 2. (3) 3. (4)Zero. Sir I waiting for your video. 🙂🙂🙂🙂🙂

[@kashafarman3142]

Sir what was that question

[@SaurabhShukla-mz1mt]

Log

[@dheerendrayadav8335]

My Answer : 256 Time taken : approx 20 seconds Information required: maine aj hi 3 raised to x = x raised to 3 wala video dekha tha Thought process : dono sides ko raised to pahle 2 fir 3 aur 4 karke dekha. 4 karne par 256 raised to x = x raised to 256 aa raha tha to mai samajh gaya solution yahi hai

[@amits4744]

I am already 30+ and not a student, but looks like this channel can become like 3Blue1Brown and BlackPenRedPen from India

[@charushashi]

Initially comparing the function with graph there will be two solutions

[@JoaoPedro-js6mk]

Guruji ek sawal hai... Kya aap complex or trigo ko ek sath krke kuch sawal Kara sakte ho... Kyu ki hame smjh me nahi ata kya kaha lagaye

[@09_i_tushargupta98]

Calculus se bhi ho jayega Log le ke zyada behtar hai Itna thodi karna hota hai.

[@amirkhursheeddar]

Why not to apply log on both side

[@zeroplays9915]

then what youll have to use Lambert W function which is not in jee syllabus

[@RishiPratap-p3r]

32

[@RishiPratap-p3r]

32

[@Prathamesh_Laddhad]

BY LOG

[@pro_gamer_yt_6126]

we can solve easily by taking log base 4 both sides

[@vishnumehra0707]

Thank u sir ji 👍🏻👍🏻💯💯💯

[@Ygsj653]

I taught some new thing of index in this video. Thank you sir.

[@ShershahSingh-hp1gc]

Is x = 3 is correct

[@mohdanas5688]

Amazing sir ❤❤

[@yuvrajkumar3961]

Sir i was able to solve this question in a different way but quite similar I just multiplied the power by 1/64 then from RHS i analyzed that x=256 But sir i am unable to understand why some people are saying that it has 3 solutions pls explain sir

[@BeautyMondal-l7o]

You are genius sir❤

[@mr.sensei1502]

Much useful

[@mrinalkumardas7974]

Just take logarithm both sides it will be solved easily.

[@zeroplays9915]

then what youll have to use Lambert W function which is not in jee syllabus

[@ajeetanand96]

Sir there will be another two values according to desmos

[@princeraj7223]

Sir log kyu nahi le sakte hai please 🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻 explain 😢😢😢😢

[@viperanuj9999]

First

[@omnatekar383]

I tried on calculator but 256 is not answer I did 4(256)-256⁶⁴=0 But answer is not getting

[@ayushverma6146]

Done by using log base 4

[@JEEASPIRANT2026-h2m]

Impossible 😂