Solving Exponential Equation

[@AdonisCreedIsrael4411]

X can solve itself.

[@KasyannoEZMath]

I love ❤️ your feedback! It gave me a loonngggg good laugh! 👍 you made my day!

[@AdonisCreedIsrael4411]

@@KasyannoEZMath Just remember that. You owe Y because it's been 100 years to solve it.

[@KasyannoEZMath]

@@user-dh6vj5pd1m okay, Adonay! Have a wonderful day 😊

[@starpawsy]

But it has to start by (a) recognising that it has a problem, and (b) WANTING to solve itself.

[@AdonisCreedIsrael4411]

@@starpawsy c. I do not care. just remember Mcnichols. ;)

[@weggquiz]

this questions uses formulas, ln(golden ratio)/ln(7/6)

[@KasyannoEZMath]

Exactly, Tutor christabel! Thanks!

[@hilmahango-yi3ht]

Thank a lot sir.. i was struggling with this.

[@KasyannoEZMath]

You're very welcome, Hilma! Have a good one!

[@kevinmorgan2317]

No need to take log to base 7/6. Just use ln or log to base 10 and the answer is identical... and quicker.

[@KasyannoEZMath]

Thanks for your feedback, Kevin Morgan. Have a great day.

[@abayomiadekanbi2123]

Kasyanno is definitely targeting larger audience. This is not a classroom where you can assume the previous knowledge of the students watching. His videos are explanatory and there's nothing wrong with that.

[@KasyannoEZMath]

@@abayomiadekanbi2123 ,that's exactly bull's eye! You're awesome! The aim of this channel is to reach out to as many people as possible the whole spectrum of people wanting to learn math the easiest way possible. This includes audience who don't have mathematics backgrounds and yet wanting to learn math and more. Cheers 🍻! Have a wonderful day!

[@kevinmorgan2317]

@@abayomiadekanbi2123 I won't disagree with that. But are you suggesting people shouldn't politely comment on the solution? That would be very odd.

[@AZ-by5ps]

You are right....should use log base 10 and obtain the answer fast, very simpla.

[@KasyannoEZMath]

Interested in learning more about different techniques in solving exponential equations, you can visit my channel and check out my playlist: Solving Exponential Equations. Thanks all!

[@shakamaos80]

Beautifull solving it reminds me of the laplace transform

[@KasyannoEZMath]

👍

[@7th_dwarf542]

very neat. Thank you for your work.

[@KasyannoEZMath]

You're very welcome, 7th_dwarf! Have a wonderful day!

[@theodoresweger4948]

Thanks for finishing the problem some leve it half done..

[@KasyannoEZMath]

You're very welcome, Theodore!

[@elliotjones3098]

this is great...very cool

[@KasyannoEZMath]

Thanks for your awesome feedback, Elliot Jones!

[@aspenrebel]

Man, Ive really forgotten my Math. I use to know all that. Ive gotten too old.

[@GeoCalifornian]

Why can’t we take the log of both sides, -at the very beginning? /Thanks in advance!

[@KasyannoEZMath]

That's a very good question, Geo. In this kind of equation, where you have all three exponential terms, the best way to do is to reduce the terms into just two exponential terms if you can't do it into just one term bearing variable exponent. You can achieve this by dividing the whole equation by any term or by factoring out. Then, you can isolate that term by itself, then take log on both sides of the equation. This is the reason why you can't take log on both sides because you can't isolate the exponential term by itself as a first step.

[@GeoCalifornian]

@@KasyannoEZMath Thank-you Kasyanno! --I really needed the answer to this question... /You're doing God's work!

[@KasyannoEZMath]

All good 👍 Geo! Have a good one!

[@ĐắcTuấnOfficial]

why don't you guys use casio for quick, why use the solution formula of quadratic equation?

[@shreyesveer8073]

It’s similar to the 4^x + 6^x = 9^x problem Answer is most probably: ln(golden ratio)/ln(7/6) Golden ratio is: (1+sqrt(5))/2 for those who don’t know

[@KasyannoEZMath]

You're exactly right, shreyesveer! Thanks for sharing 👍.

[@mikaeeldolie6215]

obviously, but it's nice to notice

[@aspenrebel]

The only thing that I can remember about logs now is that is what you throw on the fire.

[@KasyannoEZMath]

Aspenrebel, we need logs now for winter! 😁 Happy New Year!

[@aspenrebel]

@@KasyannoEZMath no Winter here, yet. 51F+ in Boston.

[@justanotherguy469]

It is very tedious, but I appreciate the way you did not make assumptions about your viewers knowledge base and skip steps. Do try and get a larger blackboard though. One more question: is a blackboard still a blackboard if it is white?

[@justanotherguy469]

Answer: yes, it's called a whiteboard Dodo! 🤪

[@KasyannoEZMath]

Thanks for your thoughtful feedback, @justanotherguy! This tutorial video covers a wide range of audiences from all walks of life, whether or not they have mathematics backgrounds. This refers to anyone who would like to learn or relearn math or anyone fascinated in solving puzzles like math problems. Have a wonderful day!

[@kennethstevenson976]

You have just exceeded my ability to solve this problem by hand.

[@KasyannoEZMath]

Glad you think so! Thanks for your feedback, Kenneth Stevenson! You're awesome! Have a great day!

[@juliangonzales5884]

This may be why I was lacking in math but why would you not move all values to one side, add/sub, and then perform log?

[@KasyannoEZMath]

That's a good question, Julian! We can't take the log if we have two or more terms containing a variable. We have to reduce the terms containing the variable into just one on one side of the equation and, on the other side, must be just one term containing just a constant. In this situation, we can now take a log on both sides of the equation and get the value of the variable. Have a wonderful day!

[@GregorShapiro]

A little more scripting and separation of the lines of your equations would make this a lot clearer.

[@KasyannoEZMath]

Thanks for your feedback, Gregor! I appreciate it 🙏.

[@slchance8839]

well done. At step 2, I divided both sides by 7^x6^x instead of just 6^x. I KNEW dividing both sides by one or both would get a different form of the equation, i just picked the wrong one. I got stonewalled later on, but forgot my second option of dividing by just ONE of the perfect squares. this was relaxing to watch. I'm sitting here, with a brandy on my balcony overlooking the view and my car below (67 corvette....it's inspiring to look at...one of my best purchases of the last 15 years!) and once you divided by 36, i stopped the video and got the quadratic trinomial (I used the letter "a" instead). At the end, I compared answers. I stopped short of the calculator but got the same radical you did. thanks for posting.

[@KasyannoEZMath]

SL Chance, that's awesome clarity of narrative that you have -- a perfect picture of a wholesome day! I like how your story flows. Thanks for your time. Have a wonderful day!

[@slchance8839]

@@KasyannoEZMath thank you for responding, and again for posting.

[@KasyannoEZMath]

@@slchance8839 all good, SL Chance! 👍. Thanks!

[@adailcavalheiro862]

You could divide by 42^x, and It would be easier.

[@KasyannoEZMath]

Absolutely! You can do that also. Thanks for sharing your idea.

[@GillAgainsIsland12]

Yes, well done. But you only need to take the log of both sides at the end, and using the rules for logarithms, get xlog(7/6) = log(1+sqrt(5)/2) and solve for x by simply dividing the log(7/6). I realize that is what you basically did, but you could have skipped those extra steps.

[@KasyannoEZMath]

Thanks for your feedback, Vincent! I appreciate it 🙏. Have a wonderful day!

[@MLDawn]

Why not just taking the log of both sides and taking it from there? Much simpler.

[@KasyannoEZMath]

I would love to see your solution.

[@matcao9962]

An alternative way If one rewrite the equation as (7^x)^2 - (6^x)*(7^x) = (6^x)^2, then we can make the right-hand side as a perfect square - to reduce three terms to two terms of this equation: (7^x)^2 - (6^x)*(7^x) + (1/4)* (6^x)^2 = (5/4)*(6^x)^2 that is (7^x - (1/2)*6^2)^2 = (5/4)*(6^x)^2 take square root of both sides and re-group the equation: 7^x = [1 +/- sqr(5/4)]*(6^x) or (7/6)^x = [1 +/- sqr(5/4)]. Now, it's easy to solve for x.

[@KasyannoEZMath]

You're awesome! Thanks for sharing your technique in solving this equation. 👍

[@jige1225]

Nice technique. May I ? [...] that is (7^x - (1/2)*6^x)^2 = (5/4)*(6^x)^2 take square root of both sides and re-group the equation: 7^x = [1/2 +/- sqr(5/4)]*(6^x) ;-)

[@prasenjitsanyal3755]

49^x-42^x=36^x, or 7^x.7^x-7^x.6^x=6^x.6^x, or a^2-ab=b^2, or a^2-2ab.b/2+(b/2)^2=b^2+(b/2)^2, or,(a-b/2)^2=5b^2/4 or, a-b/2=+-sqrt(5)b/2 or, a/b=(1+-sqrt(5))/2 or, (7/6)^x=(1+-sqrt(5))/2 Now taking log in both side xlog(7/6)=log((1+-sqrt(5))/2) .Neglecting the log of the negative term. xlog(7/6)= log((1+sqrt(5)/2) or, x=3.122

[@KasyannoEZMath]

Excellent, Prasenjit! Thanks for sharing your solution 👍! Have a wonderful day!

[@jim2376]

Just a guess: ln(golden ratio)/ln(7/6). These problems are formulaic.

[@KasyannoEZMath]

Brilliant, jim! Cheers 🍻!

[@abeonthehill166]

Great explanation ! What is the highest value of ‘pi” and to how many decimal points can it be taken to ?

[@KasyannoEZMath]

Thanks! Please be specific on what you mean.

[@aspenrebel]

The number of decimal places to which pi can be taken to is infinite. When I was a kid I memorized pi out to a lot of decimal places. I don't remember how many.

[@aspenrebel]

Pi r squared. No!! Pie are round.

[@aspenrebel]

Pi only has 1 value. .... 3.14159.........

[@goofe.washington953]

I would have as much chance of solving the problem in this video as I did back in high school with word problems. Those word problems were impossible for me, so much so that you could have written them like this: 1)John can paint 7/16ths of a house in two days 2)Bill can paint 1/7th of the house in 1 1/2 days. If they both start on the same day, at the same time, what color paint did they use?

[@KasyannoEZMath]

Two unrelated things are getting mixed up! The answer would have been any color of paint that was used. 😁

[@ourv9603]

Why is Algebra always asking us to find its EX? I mean, WHY? !

[@KasyannoEZMath]

That's a very good question, OURv! It was Rene Descartes who introduced the use of letters to stand for the unknown. Before his time, people used to refer to the unknown as the "thing." He used x, y, and z to represent the unknown value or variables in math. That representation of unknown quantities or variables carried over to the present time.

[@aspenrebel]

Wants to get those alimony payments

[@gelbkehlchen]

Solution: 49^x-42^x = 36^x ⟹ 7^(2x)-6^x*7^x = 6^(2x) |/6^(2x) ⟹ (7/6)^(2x)-(7/6)^x = 1 |Substitution: (7/6)^x=z ⟹ z²-z = 1 |-1 ⟹ z²-z-1 = 0 |p-q-formula ⟹ z1/2 = 1/2±√(1/4+1) = 1/2±√(5/4) = 1/2±1/2*√5 = (1±√5)/2 ⟹ z1 = (1+√5)/2 and z2 = (1-√5)/2

[@KasyannoEZMath]

You're awesome! Thanks for sharing your solution 👍. Have a wonderful day! Cheers 🍻!

[@iuli007]

This is more to The point

[@akky247]

I understood uptill when quadratic equation attacked !

[@KasyannoEZMath]

Not so hard to understand. It's repetitious. Have a great day, SMG Productions!

[@THEMATHREFUGE]

👍🏽👍🏽

[@KasyannoEZMath]

👍

[@equus6460]

The more accurate answer would be 3.12169771550051 These are to be solved by computers and not by humans. This is a typical regression problem to be solved.

[@KasyannoEZMath]

That's amazing, equus! Thanks for your time commenting on this video. I appreciate it very much. Have a great day!

[@lazyoldmanathome7699]

Quoting to so many decimal places is, of course, nonsense.

[@equus6460]

@@lazyoldmanathome7699 buddy providing more accurate answer is a capability that you do not possess so comment not.🤫

[@kfjfkeofitorhf9520]

X=7/6

[@KasyannoEZMath]

Kfjfk, you need to reconsider your answer. Thanks!

[@mathematic4u899]

Good

[@KasyannoEZMath]

Thanks, Mathematic4u!

[@abhishekchoudhary4689]

I never understand why they will get the numerical value after getting the ans because it is totally impractical to do this 80 percent of the time in higher mathematics answers are always in complex form.

[@KasyannoEZMath]

Numerical value was needed for the purpose of answer verification. There would be no harm if the value is converted into numerical form.

[@redouanchab3an331]

6b

[@crustyoldfart]

I don't see the point of spelling out a numerical solution. There is no indication that this is a practical problem in which a numerical solution is required. Also, having arrived at the quadratic y^2 - y - 1 = 0 , which can be written y^2 = 1 + y , the solution should be recognized by anyone with experience as the generating equation for the golden ratio phi = 1/2 * ( 1+sqrt(5) ). And we can quickly assert that x = ln(phi) / ( ln(7) - ln(6) )

[@KasyannoEZMath]

Harold Potts, that's an excellent point of view. Thanks for your time. Have a great day!

[@giftrutavi1774]

very true, the problem was created from the phi

[@anonymike8280]

It's not a piece of cake, but it's nearly pi.

[@ĐắcTuấnOfficial]

hi

[@giftrutavi1774]

The golden ratio will always appear

[@KasyannoEZMath]

Yep

[@andreluizvignamussoi1037]

log(1+5^1/2)/log(7/6) ~ 4.869

[@KasyannoEZMath]

You need to check your answer, Andre.

[@1309gsk]

you have oresebted a comolicated soloutin, the answer can ne simplfied by aviding quadratic formulae

[@KasyannoEZMath]

Thanks for your feedback, Steve!

[@abayomiadekanbi2123]

Your vocabularies are not existing in English dictionary. Simple English you can't type and you're here castigating someone else's brain racking work. What a life.

[@RakedLeaf]

we're always trying to solve something except the truth

[@profphilbell2075]

A long winded approach to a rather simple problem.

[@KasyannoEZMath]

Thanks, Phil! You're right on that. There are several ways to solve this equation, and it so happened that I chose the longer one inadvertently. I happened to see one of your videos about E=mc². The content is good , just get your camera steady. Have a wonderful day!

[@profphilbell2075]

@@KasyannoEZMath yes, you make great content. I intend to send my struggling engineering students to your channel. I do love the way you don’t miss any of the steps along the way.

[@KasyannoEZMath]

@@profphilbell2075 Hi, Phil! Thanks for your feedback! I do appreciate it 🙏 very much, sir. In my videos, I emphasize and make it clear all the steps and formula involved along the way as I solve a problem or equation. The purpose of my channel is to encourage anyone from all walks of life wanting to learn or relearn math in their own ways through KZbin videos like what I do. This means including a wide range of audiences without math backgrounds. You're awesome, Phil! 👍Thank you very much, sir! Have a wonderful day or night!

[@starpawsy]

powers of 49 will always be odd, the other two terms are always even. Thus the answer is not an integer, so I am not interested. Next video !

[@sauravkumarmishra2020]

How you find 7 / 6 Only

[@KasyannoEZMath]

7/6 is the result of dividing 6 from numerator and denominator 42/36. Thanks for visiting my channel, saurav! Have a wonderful evening!

[@joebrinson5040]

@@KasyannoEZMath yes, but why did you divide numerator and denominator by 6? [And then you apparently discarded the 6 that you divided by. ] How is this a valid algebraic operation to the equation?

[@KasyannoEZMath]

@@joebrinson5040 Thanks for your time. I don't see the connection of your question based on the solution to the exponential equation in the video.

[@joebrinson5040]

@@KasyannoEZMath sorry, you are correct. I had a brain freeze - you simply reduced 42/36 to lowest terms 7/6. My mistake.

[@MurderMostFowl]

@@joebrinson5040 he simplified the fraction… it’s like 8/6 = 4/3. You pull out a common factor, in his case 6…

[@QuynhNguyen-cw6px]

49=7.7; 42= 6.7;36=6.6; chia 2 vế cho 36^x; (49/36)^x_(7/6)^x_1=0; (7/6)^x =T; T^2_T_1=0; (T>0); T

[@KasyannoEZMath]

Excellent, Quynh! Have a wonderful day!

[@簡欽慧]

不認真

[@ЭлизаСырогина]

Слишком долго !

[@rubensramos6458]

One can find the general solution for this problem here: www.researchgate.net/publication/365126873_On_the_Solutions_of_ax_bx_cx

[@KasyannoEZMath]

You're awesome, Rubens Ramos! That's an excellent work! Thanks for your feedback.

[@rubensramos6458]

@@KasyannoEZMath Thank you. I like the problems you solve. If possible, please, show my function (Lambert-Tsallis) and my analytical solutions to your mathematical friends.

[@KasyannoEZMath]

@@rubensramos6458 you're very welcome. I will. Have a wonderful day!

[@rubensramos6458]

@@KasyannoEZMath Thank you very much. Have a wonderful day you too. I will sleep in few hours (it is 7pm now in Brazil).

[@KasyannoEZMath]

@@rubensramos6458 take care. Enjoy the rest of your day. 👍

[@idlsjay]

How does X then build a bridge?😮😳🫡

[@KasyannoEZMath]

X-men build bridges! They just remained anonymous. 😉 Happy New Year!

[@JustwaitNwatch-w]

I always understand perfectly when i see the solution step by step but i cant think how to start solving in the first place lol 🥲🥲🥲

[@KasyannoEZMath]

I exactly know where you're coming from. To get the hang of it is that you just need to do hands-on doing it, solving the equation. Repetition is the key. Write the equation, then write the solution while following the video. Then, try solving the same equation following the same solution without looking at the actual written solution you wrote based on the video. Have a great day!

[@JustwaitNwatch-w]

@@KasyannoEZMath thank you so much for a detailed explanation , i appreciate it , i will try to do it as you said 😊😊

[@KasyannoEZMath]

@@JustwaitNwatch-w you're very welcome! Thanks for watching my videos. Have a wonderful day!