Here are ten challenging problems that involve exponential & logarithmic expressions. The problems are not in any particular order (e.g. difficulty). You can download a document with the problems (and answers) using the link below. Exponents & Logarithms - Challenge Qs1. Given that x = \left(\left(\right. \left(log\right)_{8} 2 \left.\right)\right)^{\left(\right. \left(log\right)_{2} 8 \left.\right)} , find the value of \left(log\right)_{3} x .2. Given \frac{4^{x}}{2^{x + y}} = 8 and \frac{9^{x + y}}{3^{ 5 y}} = 243 , x , \textrm{ } y \in \mathbb{R} , find the value of \textrm{ } x y .