Exponential Functions

Exponential Functions: Level 2 Challenges


2x=12y,x+y= ?\large 2^x=\dfrac{1}{2^y}, \quad\quad\quad x + y = \ ?

2x=3y=12z\large 2^{x} = 3^{y} = 12^{z}

If the equation above is fulfilled for non-zero values of x,y,z,x,y,z, find the value of z(x+2y)xy\frac { z(x+2y) }{ xy }.

{ab=abab=a3b\large{ \begin{cases} ab = a^b \\\\ \frac{a}{b} = a ^ {3b} \\ \end{cases}}

a a and bb are real numbers such that a>1 a > 1 and b0 b \neq 0 , satisfying the above system.

Find ba. b ^ { -a}.

52x+55=5x+3+5x+2\large 5^{2x}+5^5=5^{x+3}+5^{x+2}

Find the sum of the solutions of xx that satisfy the equation above.

Given that x,y,zx,y,z are positive real numbers that satisfy the equations: x=yz,y=zx,z=xyx = y^z, y=z^x, z = x^y , find the value of the expression above.


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