Exponential Equation 3ˣ+9ˣ=27ˣ

[daksh]

One interesting thing about the value of y is that it is the golden ratio. And i really like your teaching method, it reminds me of bprp.

[spudhead]

I like your methodical approach, step by step, each step explained and easily deducible from the last.

[checkthisoutmathematics]

Hi TMC, thanks for an interesting problem! I was able to find the solution in the same way you did. the way in which the solution verifies the equation is also interesting considering the properties of phi. see the reply to TheFhdude. keep posting more interesting problems, TMC!

[junaidulhaque]

Sir you have to create a YouTube channel on Physics. You can do mathematics this
means can do Physics. Because mathematics is the mother of science

[FidgetMDCCLXIV]

How many different possibilities are there for x and y in the following equation:
6x + y = xy

[dngrwllrbnsn_]

It's been like 40 years since I learned the -b+-sr b2-4ac/2a and I remembered the "over 2a" before you said it! But I can't remember where the values of a b and c come from?

[gentlematicsmathstutorial.]

Wonderful 🤝
Plz which app is used for this?

[JPTaquari]

From Brazil, let's go, people!

3^X + 3^2X = 3^3X
3^X ( 1 + 3^X) = 3 ^3X

1 + 3X = 3^2X

(3^X)^2 - 3^X - 1 = zero

3^X = Y

Y² - Y - 1 = zero

Y = 1, 61 ( making báskara )

3^X = 1, 61

X = 0, 435

Bingo

Making test, the result match!
3^0, 435 + 9^0, 435 = 27^0, 435
4, 20 = 4, 20

[TheFhdude]

I think this equation has no answer. If you substitute your answer the equation doesn’t work. The reason is that 27-9 is 18 which is twice as 9. That means you have to add a bigger number than 9 (twice 9) to 9 so that it can be equal to 27. But 3 is less than 9 and there is no way you can make 3 bigger than 9 let alone twice 9 because both 3 and 9 have the same exponent x.That means if you choose a bigger x then 3 will be bigger but 9 too will be bigger by the same scale. The same goes for 27, it too gets bigger by the same scale. Since all have the same exponent x, we can ignore the exponent x and ask ourselves whether the equation 3+9=27 can ever be true and the answer is no! Hence this equation has no answer!

[danieludofia]

Hmm hi sir. It's the Herbert Einstein guy.. I love the way you gradually explain it. And it was ok. I would like you to also do things like this on physics and chemistry 🤲😅

[BartBuzz]

Actually, y can be zero if x equals negative infinity. But that is a trivial answer.

[DrHenry]

I wish you would do a discussion on what in math theory causes the creation of two solutions that are not solutions. Is math broken?

[kcii]

11 form in Belarus, we solving like this every day cuz our teacher says it is easy

[lordtiberius]

Doesn't x equal 1 solve the equation?