A math Olympiad exponential question that was solved by applying laws of indices and logarithms. #matholympiadproblem #mathcontest #mathcompetition #exponentialequations #mathematics #mathstricks
Пікірлер: 28
@RyanLewis-Johnson-wq6xs20 күн бұрын
8^(Log[2,1.25]+2)+2^(Log[2,1.25]+2)=130
@prime42314 күн бұрын
X is an exponent in this equation!!Much analysis can be done before trying natural numbers. The sum of the roots of this equation is zero. Since there is only one natural number root, the other two are probably irrational. Synthetic division is the way to eliminate long division.
@sseini14 күн бұрын
Solution dans R: X=log(5)/log(2) Il y a bien d’autres solutions dans C
@prime42314 күн бұрын
Analysis often eliminates paralysis!!
@marcgriselhubert391512 күн бұрын
Let's name 2^x = X We have then X^3 + X -130 = 0 F: X ---> X^3 + X -130 strictly increases on R, so if the equation f(X) = 0 has a solution then it is unique. As 5 is evident solution then it is the only one. So 2^x = 5 and x = ln(5)/ln(2) is the unique solution of the given equation.
@JJONLINEMATHSCLASSchannel12 күн бұрын
👏👏👏
@ExploredMaths17 күн бұрын
Nice Explanation Mam 🎉😊
@JJONLINEMATHSCLASSchannel17 күн бұрын
Thanks a lot 😊
@mathunt113018 күн бұрын
This is a cubic equation, 8^x=(2^x)^32, so y=2^x, and we're left with y^3+y-130=0. There is a formula for cubics, use that.
@mouradbelkas59819 күн бұрын
a simple solution is x log 8 + x log 2 = log 130, x = log 130 / (log 8 + log 2)
@BigFatSandwitch19 күн бұрын
I don't think log(a+b) = log(a) + log(b)
@moonwatcher200113 күн бұрын
❤
@JJONLINEMATHSCLASSchannel13 күн бұрын
❤️❤️
@user-dq3uh6ee5w20 күн бұрын
lg5/lg2.
@RyanLewis-Johnson-wq6xs20 күн бұрын
y-5 goes into y^3+y-130 y^2+5y+26 times
@mostafakubaji432415 күн бұрын
X= ln5 / ln2
@rampratap984914 күн бұрын
× = 13
@RyanLewis-Johnson-wq6xs20 күн бұрын
x=Log[2,1.25]+2
@charlesmwangi17126 күн бұрын
X =13
@shahidrasul958020 күн бұрын
Mam, plz Explain " Extraneous roots "
@Extratremendouszeus20 күн бұрын
The position of y² on top is wrong It was supposed to above the same degree (+0y²)
@JJONLINEMATHSCLASSchannel20 күн бұрын
Thanks, I will be more careful next time
@Extratremendouszeus20 күн бұрын
@@JJONLINEMATHSCLASSchannel thanks darling
@KorlinAng-bs7rh20 күн бұрын
Good teacher👍 You need to work on your checking at the very end. Do avoid using approximations as equality.
@akhlaqhusain702120 күн бұрын
pack milk is very evpensive/ hpw a mldle class person afford. the packed milk is only for rich/ in pakistan . grib jaye bhar may.