If 3 to (x -1) times 3 to (2x + 1) = 27 to y power, then y =? Many don’t get POWERS!

[@danieldennis9831]

⇒y=x First, using rule a^m•a^n=a^(m+n) the left side becomes 3^(x-1+2x+1) Next, using the rule (a^m)^n=a^(mn) the right side becomes (after ∛27 becomes 3³) 3^(3y) And finally using the rule (a^m=a^n)=(m=n) this: 3^(x-1+2x+1)=3^(3y) becomes x-1+2x+1=3y simplifies to 3x=3y which simplifies to y=x and that is my answer.

[@bradlewis8036]

Thank you for teaching this problem John. I was thinking about this kind of problem the other day and I was disappointed how I avoided the chance to learn it. Thank you so much for sharing this teaching video. More reason to buy your learning software.

[@olivemd]

I don’t recommend listening to Iron Maiden while doing math in your head. Took me 2-3 minutes to solve. By the way, back in 1967, I was a math geek. I wanted to be a math teacher, but I realized that I did not have the patience to teach.

[@bigdog3628]

NEVER listen to music when doing math. ANY instructional video has has music in it is an automatic fail. (unless of course it is an instructional video on music. But lets say that KZbin who does a walk through or how to guide for a game lets arbitrarily call "kick a dog" and he has music playing while doing this video. Instant fail)

[@m.h.6470]

Solution: multiplying two numbers with the same base means adding the exponents, therefore the left side is 3 to the power of x - 1 + 2x + 1 = 3x 3³ˣ = (3³)ˣ = 27ˣ Therefore y = x

[@lowlightevangelist9431]

I'm 48 watching your videos. Needed the encouragement, thank you. I was also too distracted and didn't care in high school.

[@tommykyle1570]

I under stand what you did, I had forgotten the power to a power rule . Remembering that rule would have made the problem easy.

[@pmw3839]

Or, from: base:3, exponent:3x = base:27, exponent:y therefore: base:27, exponent:x = base:27, exponent:y So, x = y

[@devonwilson5776]

Greetings. The answer is Y=X. From the details given, left hand side (3^X-1)(3^2X+1)= 3^(X-1 +2X +1)= 3^3X. The right hand side, 27^Y= 3^3Y. Moving forward, the left hand side of 3^3X = the right hand side of 3^3Y. That is 3^3X=3^3Y, and 3X=3Y, dividing throughout by 3 gives X =Y. Lovely.

[@bythenumbers8522]

Thank you, I do remember it from 60 years ago! 😀

[@robertroemer4233]

Since y = x then any value inserted for x in that power on the left side will = the power with the y exponent.

[@johnplong3644]

Clue Bases are the same should put the answer y=x

[@genelowry5666]

I think it's x=y

[@harrymatabal8448]

The question stayed y=. Not x=. 😂😂😂

[@johnplong3644]

Algebra 2 type problem

[@russelllomando8460]

got it - 3x=3y x=y

[@dwaipayandattaroy9801]

Sunnyu is the answer

[@ozfire7]

y=x

[@carolwhite6979]

y=-1

[@kennethwright870]

3x=3y, so x=y

[@danielmadden9691]

Y=1

[@Nikioko]

Not necessarily.

[@m.h.6470]

That is one of infinitely many possible solutions

[@peanutnutter1]

Am I right that 3 to (x -1) = 1?

[@m.h.6470]

no, why would you think that? 3⁰ is 1, but (x-1) ≠ 0, unless x = 1, which we don't know, as x is a unknown variable.

[@peanutnutter1]

@@m.h.6470 thanks for the explanation

[@Kleermaker1000]

x = y, isn't that funny? :)

[@Geoff_G]

If just watching the video and not attempting the question is wrong, then yes I will get this one wrong.

[@danielmadden9691]

I now know y can equal x in some cases

[@m.h.6470]

Actually in all cases, as you can transform the left side to 27ˣ, the equation is literally 27ˣ = 27ʸ There is absolutely no case, where x ≠ y

[@brb__bathroom]

I know what a power is in Marvel

[@harrymatabal8448]

Wtf. Y=x ok

[@harrymatabal8448]

Ok y=x all the answers were correct yet you say many get it wrong and it took you 18 minutes. Are you sure you know math

[@oldschoollew]

i got the approach correct.... turn to same base 3^(3x) =3 ^(3y) y = x but actually got the simple math wrong lol