If the equation loga (x-3) - loga (x + 2) - loga (x-1) = 1 has real roots, where a > 0, the range of a is obtained | Math enthusiast | Mathematical art

If the equation loga (x-3) - loga (x + 2) - loga (x-1) = 1 has real roots, where a > 0, the range of a is obtained

A is the bottom, a > 0, a ≠ 1
x>3
Loga (x-3) = 1 + loga (x + 2) + loga (x-1) is transformed into ax ^ 2 + (A-1) x + (3-2a) = 0
(a-1)^2 -4a(3-2a) ≥0
① - (A-1) / (2a) > 3 must have roots
②-(a-1)/(2a)

RELATED INFORMATIONS

1. The number of solutions of the equation loga (x + 1) + x = 2, (0 < a < 1) is process
2. On the equation x = loga (- x ^ 2 + 2x + a) of X, the number of solutions of (a > 0 and a not = 1) is A (0) B. 1 C 2 d change with a
3. Let loga (c) and logb (c) be two of the equations x ^ 2-3x + 1 = 0, and find the value of loga / b (c)
4. Given that 0 ＜ x ＜ 1, a ＞ 0 and a ≠ 1, try to compare the size of | loga (1 + x) | and | loga (1-x) | and write the judgment process
5. XO is the solution of the equation a ^ x = loga x (0 〈 a 〈 1), then the size relationship of XO, 1, a is
6. Given that equation a ^ x-x = 0 has two real roots, the number of real roots of equation a ^ x-loga x = 0 is Same as above, I don't think so
7. Solve the equation about X: loga (x2-x-2) = loga (X-2 / a) + 1 (a > 0 and a is not equal to 1)
8. It is known that the equation loga (x-3) = 1 + loga (x + 2) + loga (x-1) about X has real roots, and the value range of real number a is the bottom I solve it as a > = (7 + 2 √ 10) / 9 or a
9. Given the function f (x) = loga (1-x) + loga (x + 3), where 0
10. Given that the function f (x) satisfies f (x + 1) = loga (x-1) / (3 + x) (a > 0 and a ≠ 1), the analytic expression and domain of definition of F (x) are obtained
11. It is known that two of the equations x ^ 2 - (log2 B + loga 2) x + loga B = 0 about X are - 1 and 2, and the values of real numbers a and B are obtained
12. It is known that the two equations of x ^ 2 - [log2 (b) + loga (2)] x + loga (b) = 0 are - 1 and 2, and the values of real numbers a and B are obtained
13. Let f (x) = loga (1 + x) / (1-x) (a > 0, a ≠ 1) if loga (1 + x) / (1-x)
14. If f (x) = logax, (a > 0 and a ≠ 1) satisfies f (9) = 2, then f (3)=______ ．
15. Given that TaNx = - radical 3, and X belongs to (0,2), then x is? A question to fill in the blanks
16. Find TaNx when sin (x / 2) - cos (x / 2) = 0
17. It is known that TaNx = - √ 2, π
18. SiN x + cos x = 0.2 for TaNx
19. It is known that the image Q of quadratic function y = ax ^ 2 + BX + C has only one intersection point P with X axis, and the intersection point with y axis is B (0,4), and AC = B Find the analytic expression of the quadratic function Translate the image of a function y = - 3x properly to pass through point P. remember that the image is l, and the other intersection of image L and Q is C. please find a point D on the Y axis to make the perimeter of △ CDP shortest
20. It is known that the image of the quadratic function y = x2 + BX + C intersects with the y-axis at points a (0, - 6), and one of the intersection coordinates with the x-axis is B (- 2, 0). (1) find the relationship of the quadratic function and write out the vertex coordinates; (2) translate the image of the quadratic function to the left along the x-axis for 52 unit lengths, and find the corresponding functional relationship of the image