Germany| Can you solve this? | A math Olympiad exponential problem

A math Olympiad exponential question that was solved by applying laws of indices and logarithms. #matholympiadproblem #mathcontest #mathcompetition #exponentialequations #mathematics #mathstricks

[@RyanLewis-Johnson-wq6xs]

8^(Log[2,1.25]+2)+2^(Log[2,1.25]+2)=130

[@prime423]

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.

[@sseini]

Solution dans R: X=log(5)/log(2)
Il y a bien d’autres solutions dans C

[@prime423]

Analysis often eliminates paralysis!!

[@mouradbelkas598]

a simple solution is x log 8 + x log 2 = log 130, x = log 130 / (log 8 + log 2)

[@BigFatSandwitch]

I don't think log(a+b) = log(a) + log(b)

[@mathunt1130]

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.

[@ExploredMaths]

Nice Explanation Mam 🎉😊

[@JJONLINEMATHSCLASSchannel]

Thanks a lot 😊

[@marcgriselhubert3915]

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.

[@JJONLINEMATHSCLASSchannel]

👏👏👏

[@RyanLewis-Johnson-wq6xs]

y-5 goes into y^3+y-130 y^2+5y+26 times

[@moonwatcher2001]

❤

[@JJONLINEMATHSCLASSchannel]

❤️❤️

[@user-dq3uh6ee5w]

lg5/lg2.

[@RyanLewis-Johnson-wq6xs]

x=Log[2,1.25]+2

[@Extratremendouszeus]

The position of y² on top is wrong
It was supposed to above the same degree (+0y²)

[@JJONLINEMATHSCLASSchannel]

Thanks, I will be more careful next time

[@Extratremendouszeus]

@@JJONLINEMATHSCLASSchannel thanks darling

[@mostafakubaji4324]

X= ln5 / ln2

[@shahidrasul9580]

Mam, plz Explain " Extraneous roots "

[@rampratap9849]

× = 13

[@KorlinAng-bs7rh]

Good teacher👍 You need to work on your checking at the very end. Do avoid using approximations as equality.

[@akhlaqhusain7021]

pack milk is very evpensive/ hpw a mldle class person afford. the packed milk is only for rich/ in pakistan . grib jaye bhar may.

[@charlesmwangi1712]

X =13

[@ridaoueld5939]

Bullshit
Use général solving or by computing