Question

2^(3x+7)+5^(3x+4)+2^(3x+5)-5^(3x+5)=0

Answer 1

$2^{3x+7} + 5^{3x+4} + 2^{3x+5} - 5^{3x+5} = 0, \ 2^{3x}cdot2^{7} + 5^{3x}cdot5^{4} + 2^{3x}cdot2^{5} - 5^{3x}cdot5^{5} = 0, \ 128cdot2^{3x} + 625cdot5^{3x} + 32cdot2^{3x} - 3125cdot5^{3x} = 0, \ (128+32)cdot2^{3x} + (625-3125)cdot5^{3x} = 0, \ 160cdot2^{3x} - 2500cdot5^{3x} = 0, \ 160cdot2^{3x}} - 2500cdot5^{3x} = 0, \ 160cdotfrac{2^{3x}}{5^{3x}} - 2500 = 0, \ 160cdot(frac{2}{5})^{3x} = 2500, \ (frac{2}{5})^{3x} = frac{2500}{160}, \ (frac{2}{5})^{3x} = frac{125}{8},$
$(frac{2}{5})^{3x} = (frac{2}{5})^{-3}, \ 3x=-3, \ x=-1.$