Waste less time on Facebook — follow Brilliant.
×
Back to all chapters

Exponential Functions

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?).

Exponential Functions: Level 2 Challenges

         

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

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

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

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

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

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

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

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

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.

×

Problem Loading...

Note Loading...

Set Loading...