Question

(0.4)^sin3x + (2.5)^sin3x = 2

Answer 1

$(0,4)^{sin3x} + (2,5)^{sin3x} = 2 \ ( frac{2}{5} )^{sin3x} + frac{1}{( frac{2}{5} )^{sin3x}} = 2 \ ( frac{2}{5} )^{2sin3x} - 2cdot ( frac{2}{5} )^{sin3x} + 1 = 0 \ (( frac{2}{5} )^{sin3x} - 1)^2 = 0 \ ( frac{2}{5} )^{sin3x} = 1 \ sin3x = 0 \ 3x = pi n, n in Z \ x = frac{pi n}{3} , n in Z$