(3 to the m) - (2 to the m) = 65 m=? MOST won’t FIGURE OUT how to solve!

Поделиться
HTML-код
  • Опубликовано: 13 дек 2024

Комментарии • 29

  • @armchairtin-kicker503
    @armchairtin-kicker503 День назад +3

    Here's the last half of the solution, employing a system of linear equations.
    .
    let a = 3^(m/2) and b = 2^(m/2)
    a^2 - b^2 = 65
    (a - b)(a+b) = 65
    Factoring 65...
    (a-b)(a+b) = 5*13
    a - b = 5 [equ. #1]
    a + b = 13 [equ. #2]
    2a = 18 [equ. #1 plus equ. #2]
    a = 9
    Back substituting the value 9 for variable-a...
    (9) = 3^(m/2)
    3^2 = 3^(m/2)
    log(3^2) = log(3^(m/2))
    2log3 = (m/2)log3
    2 = m/2
    4 = m
    m = 4
    Therefore, m is equal to 4.

    • @Dr_piFrog
      @Dr_piFrog 20 часов назад

      This is the proper solution, not the round-robin third treatment presented in the video.👍

  • @tomtke7351
    @tomtke7351 День назад +2

    3^m - 2^m =65
    stumble around
    m=5 =>
    3^5-2^5=?65
    81×3-16×4=?65
    243-64=?65
    179 /=65
    m=4
    3^4-2^4=?65
    81-16=?65
    65=❤65✔️
    3^m-2^m=65
    ÷2^m{3^m-2^m=65}
    (3^m/2^m) - 1 = 65/2^m
    1.5^m - 1 = 65/2^m
    1.5^m - 65/2^m = 1
    X^2 - Y^2 = (X + Y)(X - Y)??

  • @rfarrelldic
    @rfarrelldic 13 часов назад +1

    solution number three is innovative but it is really trial and error again .... and if we are going to sell by trial and error error, it's much easier to just do it out right with the original equation

  • @russelllomando8460
    @russelllomando8460 День назад +4

    thanks for the lesson

  • @panlomito
    @panlomito 20 часов назад +1

    I didn't know where to start but you can still try some numbers by estimation. So I started with 3^4 = 81... quite nice!
    81 - 65 = 16 = 2^4 and bingo !!!

  • @wes9627
    @wes9627 День назад

    How about 3^m-2^m-64=0 or 3^m-2^m-66=0 or more generally f(m)=0 where m exists and is real? Iterative solution methods such as fixed-point or Newton-Raphson iteration may be used to approximate one or more values, if they exist. When m is presumed to be a posaiive integer a good place to start, since 3^m>2^m, is m=ceiling(ln65/ln3)=4, giving 3^4-2^4=81-16=65.

  • @Kleermaker1000
    @Kleermaker1000 День назад +1

    This is just the same as 81 - 16 = 65 and then transform 81 into 3^m (or 3^4) and 16 into 2^m (or 2^4). This is no real algebra imho, even though m = 4.

  • @fernandocagarrinho3980
    @fernandocagarrinho3980 5 часов назад

    How about proving that m has to be even for the result to be a multiple of 5.
    And equating prime factors of 65=5*13 to solve the difference of squares.
    That would teach something.

  • @josephlaura7387
    @josephlaura7387 День назад +2

    Thank you

  • @cyruschang1904
    @cyruschang1904 22 часа назад

    3^m - 2^m = 65
    3^4 - 2^4 = 81 - 16 = 56
    x = 4

  • @thomashawkinson7017
    @thomashawkinson7017 День назад

    Roller coaster ride! Thanks.

  • @danielduplantier3741
    @danielduplantier3741 День назад

    Serious question for the really smart people on this thread. What is the connection of this type of calculation to the ability to calculate reentry orbits?

  • @mehdizangiabadi-iw6tn
    @mehdizangiabadi-iw6tn День назад

    e^x-√x/x=0

  • @Rich.Staples
    @Rich.Staples День назад +1

    why not bring the whole equation to the (m/1) power? this would eliminate the variable power over 3 and -2 and put the 65 to the (m/1) power? u'd then end up with m=0

  • @terry_willis
    @terry_willis День назад

    This problem should be in the Math Olympiad.

    • @AINeverDies
      @AINeverDies День назад

      Well it was. I typed the problem and saw titles like "Math Olympiad (3^m) - (2^m) = 65". So probably he took the problem from that Olympiad.

  • @rarocon
    @rarocon 17 часов назад

    81 - 16 = 65 = 9² - 4² = 3² * 3² - 2² * 2² .. der Rest ist die Ausgangsaufgabe

  • @vijaybhatia2686
    @vijaybhatia2686 День назад +1

    What if the problem was 3*m + 2*m = 97 ?

    • @AINeverDies
      @AINeverDies День назад

      It's 110% easier just combine like terms, and it becomes obvious: 3m+2m=97 5m=97 m=97/5 m=19.4

  • @MrGfmassot
    @MrGfmassot 58 минут назад

    Okay.... I guess that's how you do it.

  • @DennisMcFall
    @DennisMcFall 10 часов назад

    Interesting but takes too long to get to the point/solution.

  • @AllDogsAreGoodDogs
    @AllDogsAreGoodDogs День назад

    The answer is 4. M=4.

  • @jas2819
    @jas2819 6 часов назад

    M=4. 🤗🤗 Way too easy. Me about 6 seconds.

  • @Majan-v8K
    @Majan-v8K 17 часов назад

    m= 4

  • @mauriziograndi1750
    @mauriziograndi1750 День назад +1

    3^4-2^4 = 65
    m = 4 no calculator.
    Or ln65/ln3 = 4.0 = m
    Perhaps not so academic but it works.

  • @aonghusobroin2959
    @aonghusobroin2959 16 часов назад

    4

  • @shannonmcdonald7584
    @shannonmcdonald7584 19 часов назад

    I can look at it and tell u 4. But do you want all the imaginary solutions too?