Question

Help! Exponential Equation WITHOUT CALCULATOR

Answer 1

$1. (2^{x} -2^{-x})^{2} = 4^{2} \\ \\2^{2x}-2*2^{x}*2^{-x} + 2^{-2x} =4^{2} \\ \\2^{2x}-2*2^{x-x} + 2^{-2x} =4^{2} \\ \\ 2^{2x}+ 2^{-2x} - 2=16 \\ \\ 2^{2x}+ 2^{-2x} = 18 \\ \\ 2.( 2^{x})^{3} - (2^{-x}^) ^{3}= (2^{x} -2^{-x})(2^{2x}+2^{x}*2^{-x}+2^{-2x}) \\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+2^{x}*2^{-x}) \\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+1) \\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})((2^{2x}+2^{-2x})+1)$

$\\ \\ ( 2^{x})^{3} - (2^{-x})^{3} =(4)((18)+1)= 76 \\ \\ 2^{3x}-2^{-3x} =76$