100 Inevitable Algebra Problems for Calculus

100 Inevitable Algebra Problems for Calculus! Designed for AP calculus or college calculus students, this tutorial covers a wide range of topics including factoring trinomials, polynomial long division, synthetic division, logarithmic functions, exponential functions, and more. You'll also learn techniques for simplifying complex expressions and solving partial fraction decompositions. Whether you're looking to improve your math skills or ace your calculus exams, this video has everything you need. #APCalculus #CollegeCalculus #AlgebraProblems #math #blackpenredpen
the file: www.blackpenredpen.com/_files/ugd/287ba5_88ffffbd539d419a83482923d2352fbf.pdf
with answers: remind me
BIG THANKS TO Alex Zyryanov for the timestamps!
0:00 the extreme algebra workout for calculus!
Q1 to Q10 factor & cancel
0:46 - Q1
2:05 - Q2
4:33 - Q3
6:33 - Q4
9:39 - Q5
11:52 - Q6
15:12 - Q7
23:51 - Q8
25:40 - Q9
27:24 - Q10
Q11 to Q20 expand & cancel
30:21 - 11
39:06 - 12
43:29 - 13
45:40 - 14
49:29 - 15
53:19 - 16
55:48 - 17
58:52 - 18
1:01:12 - 19
1:05:00 - 20
Q21 to Q30 using the conjugate for square root expressions
1:08:15 - 21
1:11:19 - 22
1:13:27 - 23
1:17:00 - 24
1:19:35 - 25
1:22:05 - 26
1:25:22 - 27
1:26:41 - 28
1:30:19 - 29
1:33:31 - 30
Q31 to Q40 complex fractions
1:36:13 - 31
1:39:32 - 32
1:42:30 - 33
1:44:53 - 34
1:47:32 - 35
1:49:56 - 36
1:51:41 - 37
1:54:34 - 38
1:56:36 - 39
1:59:34 - 40
Q41 to Q50 LCD & combine
2:03:16 - 41
2:05:04 - 42
2:07:43 - 43
2:10:27 - 44
2:13:03 - 45
2:17:05 - 46
2:19:52 - 47
2:22:37 - 48
2:25:56 - 49
2:29:47 - 50
Q51 to Q60 exponential & logarithm
2:34:25 - 51
2:38:06 - 52
2:42:15 - 53
2:44:48 - 54
2:46:13 - 55
2:47:53 - 56
2:49:18 - 57
2:50:29 - 58
2:53:30 - 59
2:55:40 - 60
Q61 to Q70 write in terms of x^p
2:57:23 - 61
2:59:04 - 62
2:59:58 - 63
3:01:00 - 64
3:02:58 - 65
3:04:40 - 66
3:06:00 - 67
3:08:00 - 68
3:09:09 - 69
3:12:22 - 70
Q71 to Q80 expressions from the quotient rule of derivative
3:14:09 - 71
3:16:25 - 72
3:19:29 - 73
3:22:19 - 74
3:24:10 - 75
3:26:16 - 76
3:29:50 - 77
3:32:58 - 78
3:36:29 - 79
3:39:15 - 80
Q81 to Q90 expressions from implicit differentiation (solving for dy/dx)
3:43:40 - 81
3:47:55 - 82
3:49:53 - 83
3:52:28 - 84
3:55:13 - 85
3:59:08 - 86
4:02:44 - 87
4:09:32 - 88
4:12:13 - 89
4:15:28 - 90
Q91 to Q100 solving for the unknowns from partial fractions decomposition
4:18:22 - 91
4:26:31 - 92
4:33:42 - 93
4:38:42 - 94
4:43:56 - 95
4:46:58 - 96
4:48:33 - 97
4:53:09 - 98
4:59: 46 - 99
5:04: 20 - 100
5:14:33 for the people who just want to see the end : )
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[@alexzyryanov1947]

Hope i have no mistakes 0:46 - 1 question 2:05 - 2 question 4:33 - 3 question 6:33 - 4 question 9:39 - 5 question 11:52 - 6 question 15:12 - 7 question 23:51 - 8 question 25:40 - 9 question 27:24 - 10 question 30:21 - 11 question 39:06 - 12 question 43:29 - 13 question 45:40 - 14 question 49:29 - 15 question 53:19 - 16 question 55:48 - 17 question 58:52 - 18 question 1:01:12 - 19 question 1:05:00 - 20 question 1:08:15 - 21 question 1:11:19 - 22 question 1:13:27 - 23 question 1:17:00 - 24 question 1:19:35 - 25 question 1:22:05 - 26 question 1:25:22 - 27 question 1:26:41 - 28 question 1:30:19 - 29 question 1:33:31 - 30 question 1:36:13 - 31 question 1:39:32 - 32 question 1:42:30 - 33 question 1:44:53 - 34 question 1:47:32 - 35 question 1:49:56 - 36 question 1:51:41 - 37 question 1:54:34 - 38 question 1:56:36 - 39 question 1:59:34 - 40 question 2:03:16 - 41 question 2:05:04 - 42 question 2:07:43 - 43 question 2:10:27 - 44 question 2:13:03 - 45 question 2:17:05 - 46 question 2:19:52 - 47 question 2:22:37 - 48 question 2:25:56 - 49 question 2:29:47 - 50 question 2:34:25 - 51 question 2:38:06 - 52 question 2:42:15 - 53 question 2:44:48 - 54 question 2:46:13 - 55 question 2:47:53 - 56 question 2:49:18 - 57 question 2:50:29 - 58 question 2:53:30 - 59 question 2:55:40 - 60 question 2:57:23 - 61 question 2:59:04 - 62 question 2:59:58 - 63 question 3:01:00 - 64 question 3:02:58 - 65 question 3:04:40 - 66 question 3:06:00 - 67 question 3:08:00 - 68 question 3:09:09 - 69 question 3:12:22 - 70 question 3:14:09 - 71 question 3:16:25 - 72 question 3:19:29 - 73 question 3:22:19 - 74 question 3:24:10 - 75 question 3:26:16 - 76 question 3:29:50 - 77 question 3:32:58 - 78 question 3:36:29 - 79 question 3:39:15 - 80 question 3:43:40 - 81 question 3:47:55 - 82 question 3:49:53 - 83 question 3:52:28 - 84 question 3:55:13 - 85 question 3:59:08 - 86 question 4:02:44 - 87 question 4:09:32 - 88 question 4:12:13 - 89 question 4:15:28 - 90 question 4:18:22 - 91 question 4:26:31 - 92 question 4:33:42 - 93 question 4:38:42 - 94 question 4:43:56 - 95 question 4:46:58 - 96 question 4:48:33 - 97 question 4:53:09 - 98 question 4:59:46 - 99 question 5:04:20 - 100 question

[@blackpenredpen]

Thank you very much, Alex : )

[@alexzyryanov1947]

@@blackpenredpen Thanks for the videos. You're doing a great job. Keep it up!

[@adivhahomathivha1881]

Not all heros wear capes!

[@bhavydugar6665]

@The New 3D World Fan have you heard about the law of cosines

[@Jaylenrai]

Thank you bro

[@dharunrahul1700]

You can see the dedication of this man , not by watching the whole video but by just lookin at the no. of marker boxes he has .......

[@Senerski]

i cannot believe how fun this is. I hated math for most of my life due to teachers yelling and being generally inattentive but doing this is genuinely nice thank you!

[@mathisnotforthefaintofheart]

This is awesome. I gave my Calc students 100 limit problems (on paper) and they thought the sky is falling. I looked at them and I said "sell the TV"

[@blackpenredpen]

lol

[@codeintherough]

On first read I interpreted it as become a salesperson, on second read I think you were saying stop wasting time.

[@blackpenredpen]

I only have time (and energy) to do the timestamps for each category. Could anyone please help with the timestamps for each question? I will credit you in the description. Thank you very much. 0:46 Q1 to Q10 factor & cancel 30:21 Q11 to Q20 expand & cancel 1:08:15 Q21 to Q30 using the conjugate for square root expressions 1:36:13 Q31 to Q40 complex fractions 2:02:41 Q41 to Q50 LCD & combine 2:33:57 Q51 to Q60 exponential & logarithm 2:57:23 Q61 to Q70 write in terms of x^p 3:14:09 Q71 to Q80 expressions from the quotient rule of derivative 3:43:40 Q81 to Q90 expressions from implicit differentiation (solving for dy/dx) 4:18:22 Q91 to Q100 solving for the unknowns from partial fractions decomposition 5:14:33 for the people who just want to see the end : ) Thanks for all the love and support. Thank you. bprp

[@watchoutforcopyright9339]

you are one of the youtubers that helped me ❤

[@MathCuriousity]

this is actually better than listing out all of the time stamps. I love how you categorized it!

[@kevinstreeter6943]

This is very important what he said about Calculus. The hardest part about Calculus (ignoring definition of limit) is the Algebra. It is easy if you know Algebra. If you can understand that 1/x goes to 0 as x increases without bound and you know Algebra, you should be able to learn Calculus.

[@adibgbs3136]

you're a genius! literally , Thank you for spending your time making maths fun for people all over the world. Thank you for your energy sir ! thank you for your pens :) You're an artist

[@blackpenredpen]

I appreciate your complement. Thank you!

[@haydenjones5470]

100 integrals part 2 please!!!!

[@mathisnotforthefaintofheart]

Why, you already finished?🤣🤣

[@lekiwi_4145]

EVERYONE GO !!

[@countryhumansgermany1267]

Better : 100 non-elementary integrals

[@blackwhengames_2550]

Bro you guys gonna kill him if he gotta do this much 💀💀

[@SuperYoonHo]

@@blackwhengames_2550 yeah, lol, steve needs some rest, lol

[@michaeledwardharris]

I like these longer videos quite a bit. I'm a software developer, and I just play these in the background while I'm working. I take breaks from coding to do a few problems w bprp. Quite enjoyable!

[@ryandalm]

You probably also found 1:33:22 a funny reference then!

[@adameleuch363]

@@ryandalm explain pls

[@ryandalm]

@@adameleuch363 Because in software development you also have nested elements, just like in this example (nested square root) Edit: iykyk

[@adameleuch363]

@@ryandalm ohh alright thanks

[@distressedsquid500]

"every morning: 10 sit ups 10 push ups 10 algebra problems 10 pancakes" -Chris Butler, my Calc 2 prof

[@kenetmartinez369]

For the nineth question: x^3-5x+2 = x^3-5x+2+10-10, and we can rearrange that to x^3-8-5x+10. The first part is just a cubic difference (x3-2^3) and from the second part we can factor out -5 to obtain -5(x-2). The factorization of the cubic difference is (x-2)(x^2+2x+4), so by plugging that into the the first equation we got: (x-2)(x^2+2x+4) -5(x-2). From that, we can factor out the term (x-2) to obtain (x-2)(x^2+2x+4-5) that is the same as saying (x-2)(x^2+2x-1). That (x-2) term cancels out with the other (x-2) on the denominator, simplifying our first polynomial to x^2+2x-1

[@qwertash-465]

just got into calculus and i’ve been struggling with this. THANK YOU BRO U SAVED MY LIFE

[@cesarrivas2295]

Did you pass?

[@seemslegity6093]

What a devoted mathematician, you must have great students!

[@Getsomewaterplease]

The longest video I've ever watched. It's really fun and useful. The good thing is that everything is easy

[@blackpenredpen]

Glad you liked it!

[@jaii5955]

Definitely you are the best math teacher, who actually loves to teach!

[@mtl.wraith9981]

me when the only questions i get wrong are the dumb algebra errors

[@pseudolullus]

They're not so dumb, they're the main stumbling block in calculus for a lot of people ngl

[@alexalt1215]

@@pseudolullus i think me means they can do the hard algebra, but makes stupid mistakes, like maybe factoring the sum of squares like difference of squares

[@Liwidyanto789]

Weeb

[@stephenbeck7222]

This is great. I might offer this as a summer review practice set for students going from precalc to AP Calc. But I would rewrite #81-90 with something like "A" instead of "dy/dx" since they wouldn't know what the derivative notation means and I would probably get a lot of questions along the lines of distributing the "d" and the "y" and then just solving for y. Need one for trig and one for features of graphs (end behavior, intercepts, especially for parent functions)!

[@blackpenredpen]

Thank you. I thought about using D for dy/dx for those questions but I still ended up using dy/dx... why? because honestly, I forgot to change them before I record lol!

[@stephenbeck7222]

@@blackpenredpen hah, well it is good for current calc students when they get to these topics.

[@ceb2]

he's a man of focus, commitment, and sheer f*cking will. bravo dude!

[@BlueBlaze834]

Sir I was watching your old videos and you haven't changed at all you looks same as in your old videos which is very interesting thank you sir for your hard work 👍

[@akard3022]

That was amazing . One question in the last Question, it was a mistake the CX should be -Cx samething on D sould be -D , it sould be (Cx+D)(X^2-1): Cx^3-Cx+Dx^2-D

[@ThejuTheju-l2j]

Nobody helped me in algebra even utube not suggested best one finally i found your utube thank u so much bro❤

[@sherkki9006]

Nice! Did all of these over the span of 6 hours. Now I feel a little more comfortable with algebra but not even close to becoming an algebra master.

[@ncedwards1234]

15:48 A trick I learned for the signs in expanding the sum of 2 cubes is SOAP. Same, Opposite, Always Positive.

[@annaholm9704]

YES!!!👏👏 I was anticipating this video, and he pulled through! I know this is going to be so useful for me as I'm in calc 1 now😁

[@Maths_3.1415]

I respect your hardwork sir

[@blackpenredpen]

This means a lot, especial it’s coming from you, Mr Einstein!

[@leonardobarrera2816]

Thanks Steve!!! But the equation, never will gonna have an answer, but it is your channel, I can’t do anything

[@ryandalm]

Wait I have a question 🙋‍♂️ Why would you work out the equation in question 28 (1:26:41) for example, since the final answer seems longer… or am I missing something? I can’t express how much gratitude I have for you by the way. I think we all owe you something. 😅

[@blackpenredpen]

These "algebraic moves" are mainly for calculus purposes. We do it like that for that problem at 1:26:41 is because if we are working with the limit as x goes to 6 for that expression, then we can't simply plug in x=6 (bc it will cause 0/0). But once we simply it like in the video, then we can plug in x=6 and figure out the limit.

[@blackpenredpen]

Here's an example kzbin.info/www/bejne/ipjPdWePa9Ggh80

[@ryandalm]

@@blackpenredpen this helps so much, everything makes sense now. Thank you for your time! You’re a genius Steve. Edit: I kept watching and noticed that you actually explained it here briefly too: 2:18:49 👌

[@scnt]

THANK YOU SO MUCH!!!! You are a genius!!! I love your content and I truly appreciate your efforts!! ❤✌🏻

[@大大-u3m]

The King of maths teacher !🎉

[@anacondaadultlearningcente4522]

I do love algebra. Doing algebra is soothing to my brain.

[@ronieespinosa8710]

Thanks to you, I have learned how to factor cubic equations. I always have a hard time in those.👊👊👊

[@amiteshsaini492]

This man is the reason why I am passing math

[@kameshxyadav]

Please teach us how to sketch graph of most of the functions and curves The graphical approach in differential calculus seems much helpful and time saving

[@daddy_myers]

You can learn to sketch stuff pretty easily using Calculus, even graphs which you've never seen before; you should definitely give that a look if you're comfortable with Calculus 1.

[@Vinaya999]

I have been learning how to solve differential equation but I struggle a bit with integration this is really helpful.❤😊

[@BLANIE]

just a while ago I completed practising those questions, which I solved using different methods than those you have shown, the adventure was long but I learnt a lot of new ideas on how to solve these equations, and you kinda proved my idea that every question has infinite way to solve it, which I liked, also thanks for your time

[@ITWorksSoftware]

3:13:18 #70: middle term should be -24^-3/2 not -24^-3/4 right?? Or am I wrong? 🧐

[@timbo2089]

right

[@armyofmc1]

Hi I am a big fan and I just got the integrals for you t-shirt with + constant or just +c on the front and I would just like to say hello from Canada I am 13 and love your videos and I will continue to support them I’ve been watching them for a while now since last year and I am very impressed by your skills in mathematics

[@jonathancole6826]

Sleepy pen hungry pen, you are purely genius. I learn something new each time you have new videos

[@PrudentialViews]

WOW blackpenredpen, you are so close to 1,000,000 subscribers! Keep going with the hard work. :)

[@blackpenredpen]

Thank you!

[@PrudentialViews]

@@blackpenredpen No problem!

[@ปาริชาติแซ่ย่าง-ค4ฝ]

So hard for me at school grade 9. But 15 years ago, today is so nice of enjoying mathematics

[@kore675]

I really needed this ty ty :)

[@tmann986]

I should procrastinate my studying by watching you do these problems 😂

[@whamjampamham]

I am watching this complete tutorial. Please can you also make a full calculus playlist. Calculus 1, Calculus 2 and Calculus 3. It gets confusing and scary when I see the channel videos and I don't even know where to start.

[@jacksonzhu4282]

it's definitely a unique tutorial, love you brother!

[@ShaunakDesaiPiano]

31:51 I know it’s not the method we should be using, but we can use the difference of squares and difference of cubes formulae and get the result without actually doing any expanding. Rather, the opposite - we factorise and cancel!

[@boidaemon8733]

do you think you could ever do 100 calculus 3 questions, it would really help me and others out, love ur vids anyways

[@fabianperdomoborja8623]

Excellent, perfect to repast _Saludos_ 🤝 from Colombia 🇨🇴

[@darshbir]

Thanks this will help for my college entrance exams 👍

[@souhamghosh8714]

Yesss, here we go!!!

[@darabqureshi3184]

yay, ive been waiting for this one!!!

[@ITWorksSoftware]

I’ve worked out all this with you twice now! Whew! 😂

[@joshhauss98]

This is exactly what i need thank you

[@ThejuTheju-l2j]

you are the best my teacher i will never forget your help thank so much.may lord bless u have a blast future

[@JMCoster]

This workout was extreme for you (in fysical terms :)) But nevertheless many thanks ! for your hard work.

[@frankgetachew1833]

Thanks alot you're my best of best youtuber

[@jalalgk2415]

waiting it for 5 hours😂😂tnx

[@brucefrizzell4221]

I am glad to learn what Pascal's Triangle is used for .

[@blackpenredpen]

Nice!

[@r.i.p.volodya]

I love the way you say "cancelleded" 😁

[@devoid_x]

Great video! This has been an awesome review for algebra. I think there is an issue with the final answer of question 70, the exponent of -3/4 for -24x should be -3/2. 1/2 - 2 = 1/2 - 4/2 = -3/2

[@prajeshchakraborty9205]

My favorite Video ever 💖😃

[@rmontcal]

Hi bprp - math teacher here and big fan! Is the file of questions still available somewhere? Thanks.

[@tommyindrajaya1266]

Same question!

[@dilinapramodya]

Thanks man.really appreciate this.

[@matematicadosucesso]

the best one!, bless you brother,

[@erlingnesbakken9871]

I love this so much. This dude is so sweet!

[@josefschmid7713]

Unfortunately, I can't acces the document anymore. By chance is there an alternate upload somewhere?

[@waldoemerson8676]

Why not wear the mic? Or headset? Something to think about. Thanks for the video!

[@mikejackson19828]

1.00am? I hope you had plenty of caffeine, Steve! 👍

[@nethnidilshara550]

Thank you 💕

[@neo-v0rtex86]

#3 is better with (x + 7)/(2 - x), looks more perfect. :D

[@MPOLLACCHI1]

I love your shows thank you

[@vigoolz241]

at 3:13:13 shouldn't it be x^-3/2 ? because 1/2 - 2 is same as 1/2 - 4/2 which is -3/2

[@lunaas1029]

Yes I was looking to see if someone else found that

[@michaelroberts694]

76 should be (1+x^2)^(-5/2); love the video

[@michaelroberts694]

Also for 100, D=-1 (not 1)

[@freezingfusion]

Brilliant! I'm confused about the last question though. When multiplying out (Cx+D)((x^2)-1), he gets (Cx^3)+(Cx)+(Dx^2)+(D), whereas I got (Cx^3)-(Cx)+(Dx^2)+D, and I get D=-1 instead of D=1. Am I wrong?

[@jefferyannor6116]

X^2 +1 not -x^2-1 It was rather

[@jan-willemreens9010]

...Question 22: (sqrt(2x + 9) - 5)/(2x - 16) (rewrite the denominator 2x - 16 as follows: 2x - 16 = (2x + 9) - 25, and treat it as a difference of squares: 2x - 16 = (2x + 9) - 25 = (sqrt(2x + 9) - 5)(sqrt(2x + 9) + 5), and then cancel the common factor (sqrt(2x + 9) - 5) of the numerator and denominator to obtain the final result of: 1/(sqrt(2x + 9) + 5)... Jan-W

[@nethnidilshara550]

Thank you so much.this is great.❤❤

[@nitinsaini1236]

using integration find the area of triangular region whose sides have the y=2x+1 ,y=3x +1 and x=4.

[@QuantitativeDiaries]

100 differential equations!!

[@mikejackson19828]

I'm not taking any classes. I'm just interested in maths.

[@redweg47]

Thank you

[@13arpanbagchi43]

100 algebra part 2 plssss

[@mirza00]

This guy is just awesome

[@jan-willemreens9010]

...Question 21: (sqrt(x) - 8)/(x - 64)... An alternative way is to treat the denominator x - 64 itself as a difference of two squares as follows: x - 64 = (sqrt(x) - 8)(sqrt(x) + 8), and then cancelling the common factor (sqrt(x) - 8) of numerator and denominator, resulting in: 1/(sqrt(x) + 8); same result, but without using the conjugate method... Jan-W

[@tracert6804]

There are some small mistakes in the answers document (but the video has the correct answers) : Q06 wrong sign in denominator, it should be 2/(x+3)(x+5) instead of 2/(x+3)(x-5) Q25 denominator has 5x twice instead of 5x + 5h Q59 there's a plus sign instead of a minus sign between the terms, so 3/2 + 1/4 log4(x^3 +2x + 5) should be 3/2 - 1/4 log4(x^3 +2x + 5) Q60 left term lacks the x, so 1/3 - ln(x^2 + 1) should be x/3 - ln(x^2 + 1) Q66 there's an exclamation mark instead of a 1 lol Q68 same as above Q74 denominator lacks 2 * sqrt(x) Q90 denominator has plus instead of minus

[@blackpenredpen]

Thank you so much. I just fixed them on my file and will upload them soon. I really appreciate it.

[@Exonorm27]

I don’t see the issue with 25 tho?

[@francoischauvelin]

Although it doesn't affect the answer, C in question 98 should be 1 (5/5) instead of 3.

[@wepped482]

This is where we forget to get into the habit of clarifying that x≠ values where the equation wouldn't work... so equations are 'strictly the same' although if you plug it into the original equation it wouldn't work and make you divide by 0.

[@3koningen]

Thank you.

[@smartsidemotovation425]

could you please put a link for the file because that at the description is not working , thanks for your work

[@itznidal9501]

3:39 why do you not cancel out the 3?

[@saharhaimyaccov4977]

3:22:00 this just the d/dx of sqrtx / (1+x²)

[@dkianz]

So nice! You should make a video of an equation using tetration (hyper-4)!

[@SuperYoonHo]

Thank you!!!

[@monkeymogul7505]

This is AMAZING!!!!

[@nvapisces7011]

When I saw algebra I thought this is going to help my Linear Algebra 1 Mid Term Exam tomorrow but its just basic algebra hahaha oh well

[@ItsPungpond98]

8:49 Suddenly, the audio became better

[@Maths_3.1415]

Yes

[@chillvibez7913]

@@Maths_3.1415 sir big fan

[@Maths_3.1415]

@@chillvibez7913 :)

[@SuperYoonHo]

@@chillvibez7913 LOL🤣🤣

[@limyuwei04]

For the first few (factor and cancel) i think it would be better if you give a domain for x

[@artsmith1347]

This has been important in other videos. The first equation, as given, is not defined at x = 7, but there is no restriction on the simplified version after canceling. I guess it is okay in this case because the limit of the given equation as x approaches 7 is 4 and the simplification gives the same answer.

[@09Maggio]

I followed all the video and I thank you for uploading this, but I don't understand something: question 100, minute 5:09:05, isnt it supposed to be Cx^3 - Cx + Dx^2 - D? Why is there Cx^3 + Cx + Dx^2 - D?

[@eseo0301]

I was wondering the same thing. I also got Cx^3-Cx+Dx^2-D and D=-1.

[@guilhermerocha2832]

Can you solve the following equation: 2^x = i Thank you, and great job!!

[@Apollorion]

I know a way how to do that, so I think BPRP knows too. edit: The solution is x=i*pi*(1+4k)/ln(4) with k being any arbitrary integer. And here's why: we begin by putting e in the base: a) 2^x=e^(x*ln(2))=exp(x*ln(2)) b.1)exp(i*2*pi)=1=exp(0)=exp(2*i*pi*k) (I can divide & multiply a number by 1 as many times as I want, so k can be any integer.) b.2) i=exp(i*pi/2)=exp(i*pi*(1+4k)/2) (Verify the first two b equalities by taking a look at the unit circle of the complex plane and don't forget Euler's formula: exp(a+bi)=exp(a)*(cos(b)+i*sin(b)) ) a) and b.2) combined tells us: 2^x=exp(x*ln(2))=i=exp(i*pi*(1+4k)/2) And if y=y then f(y)=f(y) so x*ln(2)=i*pi*(1+4k)/2 => 2^x=i Divide LHS & RHS by ln(2) and pull that 2 into the logarithm and you get my proposed result: x=i*pi*(1+4k)/ln(4) k being any integer.

[@punditgi]

Awesome! 🎉😊

[@bigbadbith8422]

Absolutely brilliant- now, lie down.

[@fvai8203]

Try checking chapter p.6 old exams by KFUPM (a uni). They have some pretty good and tough factoring problems.

[@amitabhnair460]

Make a video of 100 question on difnite integration and take tough question