Algebra
Exponential Functions
\[\large 2^x=\dfrac{1}{2^y}, \quad\quad\quad x + y = \ ? \]
by
Trevor Arashiro
\[\large 2^{x} = 3^{y} = 12^{z} \]
If the equation above is fulfilled for non-zero values of \(x,y,z,\) find the value of \(\frac { z(x+2y) }{ xy }\).
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 \( b ^ { -a}. \)
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.
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.
by
A Former Brilliant Member