Unique Exponential Equation | How To Solve The Exponential Equation Problem | Aman Sir

Today we will Solve a Unique Exponential Equation, which will surprise you.

In this video, we will discuss the exponential equation problem and we will learn how to solve the unique exponential equation.

this exponential equation is picked from an exam from Russia, and also these types of problems are often asked in JEE advanced exam.

This question is a good revision of JEE Advanced level Exponential equation question & will surely help you learn good concepts of the Exponential equation.

Let's see the simplistic solution by Aman sir to this Unique Exponential Equation.

so watch this full video and learn how to solve these types of exponential equations and what type of concept and method we will use to solve this exponential equation.

Solve This Exponential Problem

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[NIRAjKUMARबिहार]

Mai aapke jaisa Genius Ban ne ki kosish ker raha hu
Mai bhi ab doubt questions solved kerne laga apne youtube channel per sir

[debmukherjee]

Sir you have the spirit that every student wants in their teacher. We want more topic wise JEE mains and advance question discussion and explanation.

[mathq]

Hero Of Mathematical world 🌎.!
He Has Its Own Style Of Teaching Mathematics ..!!
We Can Say a Unique Style Of Teaching Mathematics.!!

[arnavverma]

Sir, i have an alternate and much easier approach, take x²= t and substitute in given equation to simplify powers. Then take log with base 2 on both sides of equation, and it will be converted to a simple cubic equation in t with root t=1, which gives x= 1, -1, not able to solve for x=0 but that can be checked by substitution in initial equation 🙂

[KoushikDas]

5:40 complications start from here.
Itna karne ka jaroorat hi kya tha sir itna AM GM uske andar ghusne ki ...isko directly log Wale se v kar sakte the

[rohitkhatri]

I tried and did it in first attempt... felt great, thank you Aman Sir for such videos!!❤

[dhananjaysharma]

Sir please bring questions from AIME, Canadian MO, Bulgarian MO and IOQM

[ultra_]

Did it using the basic exponential laws without using AM GM inequality. A smart 10th grade student can surely do this too. Wonderful question.

[hitarthvachhani]

in this type of question always first try hit and trial method!! it worked here! 1 and -1 and 0 are most common numbers for hit and trial

[factshut]

simple trick of these type of questions - in AM and GM equality holds in all those questions in which we have find the proper value of the terms so equate both terms you will get the value of x
This trick works on all these type of questions .🙂

[arpitsamantaray]

Sir I have seen this question and this is an amazing question of solving exponents, i have find a method to solve this question, so first take 2 ^x^4+1 to the denominator of 2^x^6 + 2^x^2 so we get 2^x^6+2^x^2/2^x^4+1 as 1 and we can now seprate it and as know the property of exponents we can write 2^x^6-x^4-1 + x^2-x^4-1 =1, we know only x^6-x^4-1 and x^2-x^4-1 can have a single value of -1/2 to satisfy the equation, so then we can solve x^6-x^4-1 by simplifying it as (x^2)^3-(x^2)^2-1=-1, let x^2 = t we can get two values of t as o and 1 and then substituting t as x^2 we can get x as o and +1or -1. Again thanks sir for coming with such type of nice questions .

[mansakundu]

Done it by simple exponent steps from the concept of class 7

[KoushikDas]

Sir yeh question maine just by equating the exponents mein kiya ho v gaya answer.
I don't know if this process is correct or not but answer is coming -1, 1, 0 . I have tried the logarithmic process also but i did some mistake out there.
Writing it at 0:30. Let's see the other methods.

[tusharkumar]

I solved this question by dividing 2 ki power x^2 and then LHS me 1 bna liya, 2 ki power something minus 2 ki power something ayega equal to 1 or ye tabhi satye h jab phele wala something equal to 1 ho or baad wala something equal to 0 ho vaha se x ki values ajayegi

[vaibhavsrivastava]

I figured the answer within a minute, cuz I remembered my past encounter with an exponential eq. q... I think it was from probability or pnc exercise (numerical type) of vikas gupta . My learning from it was that when two exponents of base 2 can be conveniently added or subtracted to give another exponent in same base, i.e. 2 when their powers are same (in case of addition) and at a difference of 1 (when being subtracted, cuz then u get a 1/2 factor which can incorporated as -1 power) .... so i straightaway equated x2 and x6, which gave meaningful answers, or else i would have further tried taking one of the terms to RHS and tried creating that difference of 1

Anyway, sir ur solution was also great, and I will try to approach with am gm also now in such q.s

[aaryanpatel]

What about +- i (iota) question mein kaha bola hai ki real solution

[nikhilmahajan]

sir mile hai mujhe
Bas itna kehena chahunga 1 dum bhannat😎

[Swayamkhairnar]

Sir please continue such videos
As I love maths

[cascabellah]

Sir u made me fall in luv with mathematics ✨🌼

[tanaykumar]

Sir, I am glad that you have being such a amazing equation in the eq the first step was the toughest.plz in future it will be helpful that you can make a video on how to identify the application of am and gm in a perticular equation.