\( \begin{array}{ll}\text { a) } 1+2^{1-2 x}=4,5 \times 2^{-x} & \text { b) } 3^{-2 x}+8.3^{-x}=9 \\ \text { c) } 5^{x}+5=2.5^{2-x} & \text { d) } 2^{x}=2^{4-x} \\ \text { e) } 10^{x}-11+10^{1-x}=0 & \text { f) } 3^{2-x}+2^{3}=3^{x}\end{array} \)

To solve the equations involving exponents, it's essential to recognize that exponential functions have specific properties that can simplify your work. For instance, when you're dealing with equations like \( 2^{x} = 2^{4-x} \), you can equate the exponents directly, leading to a straightforward solution. Using logarithms can also help transform products and powers into sums and products, making complex equations much easier to manipulate. Remember that when working with bases that are different, like in equations involving \( 3^{2-x} \) and \( 2^3 \), converting everything into a common base or using logarithmic properties can often be the key to untangling your problems. It’s easy to make a mistake by misapplying exponent rules, so always double-check that you’re applying to the entire expression!