MHB Solve Exponent Problem: 3^x=4^y=12^z

  • Thread starter Thread starter Bushy
  • Start date Start date
  • Tags Tags
    Exponent
Bushy
Messages
40
Reaction score
0
Given [Math]3^x=4^y =12^z[/Math] show that $$z=\frac{xy}{x+y}$$

I've take logs on both sides and find myself going in circles, any hints?
 
Mathematics news on Phys.org
$$3^{xy/(x+y)}=12^{zy/(x+y)}$$

Now try using the fact that $3$ and $4$ are factors of $12$ and that $4^y=3^x$.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Show x³y+y³z+z³x is a constant
Replies
1
Views
1K
MHB Solving System of Equalities: x^2-y\sqrt xy & y^2-x\sqrt xy =3
Replies
2
Views
1K
MHB Solve System of 4 Equalities: x+y+z+w=22, xyzw=648
Replies
6
Views
1K
MHB What is the Sum of x, y, and z in a Non-Negative Real Number System?
Replies
4
Views
1K
MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
Replies
1
Views
1K
MHB Solve System of Equalities: x^2+xy+y^2, x^2+xz+z^2, y^2+yz+z^2
Replies
7
Views
1K
MHB Is There an Exact Solution to the Equation \(4^x + 3^x = 12\)?
Replies
7
Views
1K
MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
Replies
1
Views
995
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
Replies
1
Views
1K
MHB Challenge Problem #7: Σ(x/(y^3+2))≥1
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top