examples, and problems from the community.

including olympiad champions, researchers, and professionals.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

From compound interest to bubonic plague, things that grow or spread really fast are often modeled by exponential functions. Learn about these powerful functions (pun intended?).

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

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Trevor Arashiro**

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

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

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Swapnil Das**

\[\large{ \begin{cases}

ab = a^b \\\\
\frac{a}{b} = a ^ {3b} \\ \end{cases}} \]

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

Find \( b ^ { -a}. \)

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Sharky Kesa**

\[\large 5^{2x}+5^5=5^{x+3}+5^{x+2}\]

Find the sum of the solutions of \(x\) that satisfy the equation above.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Yan Yau Cheng**

Given that \(x,y,z\) are positive real numbers that satisfy the equations: \(x = y^z, y=z^x, z = x^y \), find the value of the expression above.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Mrunang Kothari**

© Brilliant 2017

×

Problem Loading...

Note Loading...

Set Loading...