Question

При каком значении x произведение 2^2x+1 * 3^3x+5 равно произведению 4/3 *9^x+1 * 8^x+1

Answer 1

2^(2x +1)*3^(3x +5) = 4/3*9^(x+1) *8^(x+1)
2^(2x +1)*3^(3x +5) = 4/3*3^(2x +2)*2^(3x +3) | : 3^(2x +2)*2^(3x +3)
3^(x+3)/2^(x + 2) = 4/3
3^x*3^3/(2^x*2^2) = 4/3
3^x*27/2^x*4 = 4/3| *4/27
(3/2)^x = 14/81
(3/2)^x = (3/2)^-4
x = -4