Question

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

Answer 1

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