Given x > 10, Y > 10, xy = 1000, find the value range of (lgx) (lgY)

y=1000/x ∈(10,100)
x=1000/y ∈(10,100)
(lgx)(lgy)=(lgx)(3-lgx)=-lg²x+3lgx=-(lgx-3/2)²+9/4
∵x∈(10,100)
∴lgx∈(1,2)
∴(lgx)(lgy)∈(2,9/4)

RELATED INFORMATIONS

1. Factorization of M (m-n) - n (n-m)
2. To verify Goldbach's conjecture with VB programming, that is, an even number greater than or equal to 6 can be expressed as the sum of two prime numbers Try not to use too complicated and high-end sentences. We haven't learned many of them Private Sub Form_ Click() Dim a As Long,b As Long,c As Long,i As Long,t As Long c = a - b Do A = Val (InputBox ("input not less than 6 even")) Loop Until a >= 6 And a Mod 2 = 0 If (b = 2 Or b = 3) And (c = 2 Or c = 3) Then Print a + "=" + b + "+" + c Else For i = 2 To Sqr(b) If b Mod i = 0 Then For t = 2 To Sqr(c) If c Mod t = 0 Then Print a + "=" + b + "+" + c Next t Next i If i > Sqr(b) Then If t > Sqr(c) Then Print a + "=" + b + "+" + c End If End If End Sub Seek correction
3. In △ ABC, ∠ ACB = 90 °, M is the midpoint of AB, ∠ PMQ = 90 °, indicating: PQ & sup2; = AP & sup2; + BQ & sup2; P is on AC, q is on BC, I don't have a picture, but I can draw it myself,
4. As shown in the figure, in the parallelogram ABCD, e and F are on the sides of AD and BC respectively, and AE = cf. the following results are obtained: (1) the △ Abe ≌ △ CDF; (2) the parallelogram bfde is a parallelogram
5. When passing through P (5, - 3), the angle of inclination is a, and cosa = - 3 / 5, the intersection circle x + y = 1 is located at P1 and P2, the coordinates of chord midpoint of PP1 * PP2 and p1p2 are calculated (with parameter Square) P1P*PP2=t1t2=330
6. The length of one side edge of a triangular pyramid is 16 cm, the length of the opposite edge is 18 cm, and the length of the other four edges is 17 cm
7. Given that the maximum value of quadratic function F X = kx2 + 2kx + 1 in the interval [- 2,2] is 9, find the value of real number K
8. How to lay the floor of 5m long and 3M wide with two triangular floors with right angle sides of 30cm and 10cm respectively? How to lay the floor of 3M wide and 5m long?
9. In the triangular pyramid p-abc, it is known that PA = Pb = PC = 2, ∠ BPA = ∠ BPC = ∠ CPA = 30 ° and the shortest distance of a rope from point a to point a is______ ．
10. If the distance between the point P (4, a) and the line 4x-3y = 1 is not greater than 3, then the value range of a is () A. [0，10）B. （0，10]C. （-10，0]D. [0，10]
11. Inequality a1 + A2 / 2 ^ 2 + A3 / 3 ^ 2 +... + an / N ^ 2 ≥ 1 + 1 / 2 +... + 1 / n
12. Simplification ratio: 84:162 =? Ratio: 1 / 2: 1 / 8 =? 3 / 4: 7 / 12 =? 1 / 5: 1 / 20 =?
13. Two sides of the equation multiply or divide by the same non-zero number to form the left and right sides?
14. Is this pair of glasses your~ Yes, it is. Or yes they are
15. This pair of glasses is mine. Why use is instead of are
16. this pair of trousers is too short for the boy to ____ a. Put it on B. put on why not choose B? This question is for B. Is it because it's a sentence. There's no shortage of anything in the back
17. Is the predicate after "either" or "neither" singular or plural Neither of her legs are / is strong enough,
18. Is the predicate verb singular or plural
19. There is a shirts, a pair of pants in the red ward
20. Is a pair of scissors singular or plural