Math Olympiad Exponential | How To Solve 16^x+12^x=2.3^2x | Challenging Mathematics Question.

[@trojanleo123]

I think the numerator of your final answer can also be further simplified as ln(2) + iπ

[@HeywoodUmanoff]

Very nice! Thank you. 😊

[@userr717]

Please keep up making these kinds of videos☺️

[@onlineMathsTV]

Alright ma, We will do our best possible to serve you better with content like this as requested. Much love ❤️❤️💖💖💖💕

[@embracinglogic1744]

It is amazing how much more math I learn on KZbin than in school. For example, in school I was told that Euler's formula e^{pi*i} + 1 = 0 was so beautiful, but never saw any applications. Here, I see a direct application.

[@wes9627]

58 years ago I was studying for a degree in electrical engineering. Fixed-length complex vectors were used to represent AC voltage and current, and they were called rotating phasers. In a purely resistive circuit the voltage and current are in phase, so their rotating phasers are aligned. An inductor causes the voltage phaser to lead the current phaser, and a capacitor causes the current phaser to lead the voltage phaser as they spin around. This is the tip of the iceberg of what one can accomplish using Euler's equation.

[@Lokeshkumar-jk8ib]

Nice

[@SemsatMammedowa-v3m]

It is amazing ❤

[@danielfranca1939]

Great one bro. Thanks for this clip again. More grace bro

[@onlineMathsTV]

Appreciated

[@jidraffgithendu7546]

Can you simplify further this expression?

[@MeinhartKöster]

wonderful, i failed to use euler equation and stopped with the negative 2

[@kanimozhaisabareeswaran3180]

Super

[@onlineMathsTV]

Thanks my friend for watching and commenting. We love you dearly my friend...💖💖💕💕😍

[@bandarusatyanandachary1181]

Insted why can't you apply the formula that: if a^x = m then logm to base a = x

[@wes9627]

Don't use "." to represent multiplication because it is too easy to interpret as decimal. It is more common to use "*". I interpreted 2.3^2x as (2.3)^2*x and you interpreted it as 2*3^(2x). I always use "()" when operator order may not be clear. I always try to solve problems before looking at the published solutions. If a problem is not clearly stated I may be wasting my time trying to solve a more difficult or unsolvable problem. My approach to this problem is to solve 16^x+12^x-2*9^x=0. Divide this equation by 12^x to get (4/3)^x+1-2*(3/4)^x=0 and substitute y=(4/3)^x giving y+1-2/y=0. Rearrange to y^2+y-2=0 and solve for y=(-1±3)/2=1 or -2 Thus, (4/3)^x=1 or (4/3)^x=-2. In the first case, x=0, which could have been deduced by inspection. In the second case, x=ln(-2)/ln(4/3)=(ln2+iπ+2ijπ)/ln(4/3), j=0,±1,±2,...

[@onlineMathsTV]

Ok sir, noted and thanks for this wonderful correction sir.

[@chuksnonso2320]

Great video, but try to utilize time sir.

[@onlineMathsTV]

Ok. Thanks

[@magdiragheb8087]

16ⁿ+12ⁿ=2.3²ⁿ 2⁴ⁿ+3ⁿ.2²ⁿ=2.3²ⁿ (2²ⁿ)²+3ⁿ.2²ⁿ-2.(3ⁿ)²=0 Put v=2²ⁿ , u=3ⁿ v²+uv-2u²=0 (v+2u)(v-u)=0 v=u or v=-2u refused 2²ⁿ=3ⁿ -> n=0