Question

Решите показательное уравнение

Answer 1

$2^{3x+10} -3^{3x+9}+3^{3x+7}+2^{3x+9} =0 \\\\2^{3x+10} +2^{3x+9} =3^{3x+9}-3^{3x+7}\\\\2^{3x+7}(2^{3}+2^{2} )=3^{3x+7}(3^{2} -1) \\\\2^{3x+7}\cdot12=3^{3x+7}\cdot8\\\\\\\dfrac{2^{3x+7}\cdot12}{3^{3x+7}}=\dfrac{3^{3x+7}\cdot8}{3^{3x+7}} \ ; \ 3^{3x+7}\neq 0\\\\\\12\cdot\Big(\dfrac{2}{3}\Big)^{3x+7} =8\\\\\\\Big(\dfrac{2}{3}\Big)^{3x+7} =\dfrac{8}{12}\\\\\\\Big(\dfrac{2}{3}\Big)^{3x+7} =\dfrac{2}{3}\\\\\\3x+7=1\\\\3x=-6\\\\\boxed{x=-2}$