Understanding the Exponential Equation 2^(2x+y) = (4^x)(2^y)

  • Thread starter Thread starter PsychStudent
  • Start date Start date
AI Thread Summary
The equation 2^(2x+y) = (4^x)(2^y) holds true due to the properties of exponents. By substituting values for x and y, the equivalence can be verified, demonstrating that both sides yield the same result. The discussion highlights the rules of combining exponents, specifically x^a * x^b = x^(a+b) and x^(ab) = (x^a)^b. Understanding these rules clarifies why the initial equation is valid. This foundational knowledge is essential for solving similar exponential equations.
PsychStudent
Messages
9
Reaction score
0
Is 22x+y = 4x2y? If I substitute various digits into the x and y variables, it works, but I can't understand why. Can anyone please explain this to me?

For example, if we choose x=3 and y=1,
2(2)(3)+1 = 27 = 128
2(2)(3)+1 = 4321 = 64(2) = 128

Thanks
 
Mathematics news on Phys.org
It follows from the basic rules of combining exponents.

x^a x^b = x^{(a+b)}

x^{ab} = (x^a)^b
 
I can't believe I didn't figure that out. Thank you!
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
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 »

Similar threads

MHB How Can You Rewrite an Equation to Express y as a Function of x?
Replies
3
Views
1K
MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
Replies
1
Views
1K
MHB Prove Inequality: IMO $\frac{1}{x^4}+\cdots \geq \frac{128}{3(x+y)^4}$
Replies
5
Views
2K
MHB Solve Equation: $x^4+2x^3-x^2-6x-3=0$
Replies
7
Views
1K
MHB Circle Equation: Solving for x^2 + y^2 + Ax + By = 0 w/y=4/3x
Replies
2
Views
1K
MHB Challenge Problem #7: Σ(x/(y^3+2))≥1
Replies
2
Views
2K
MHB Challenge problem #1 Solve 2x^2y^2−2xy+x^2+y^2−2x−2y+3=0
Replies
4
Views
1K
MHB Solve System of 4 Equalities: x+y+z+w=22, xyzw=648
Replies
6
Views
1K
MHB Win a $10 or $5 Prize in Tom's 4/19 Lottery Fundraiser
Replies
1
Views
2K
MHB Solve for x and y When (x+$\sqrt {x^2+1})\times (y+\sqrt {y^2+4})=7$
Replies
1
Views
971

Hot Threads

Recent Insights

Back
Top