Find the value range of X in log (2-x) (x + 3). (2-x) is the subscript

Find the value range of X in log (2-x) (x + 3). (2-x) is the subscript

2-x > 0 and not equal to 1, so x0 x > - 3
So - 3

Find the logarithm with 1 / 2 of the root sign as the base (4 * 8)

The logarithm with the base of 1 / 2 of the radical (4 * 8)
=lg32/(lg√1/2)
=5lg2/(-1/2lg2)
=5/(-1/2)
=-10

2 to the 31st power and 3 to the 21st power, without logarithm, how to compare the size?

3 to the 21st power / 2 to the 31st power = (3 / 2) to the 21st power / 2 to the 10th power
(3/2)²=9/4=(2+1/4)
The 21st power of (3 / 2) / the 10th power of 2 = (2 + 1 / 4) times (3 / 2) / the 10th power of 2 > (3 / 2) times (2) / the 10th power of 2 = 3 / 2 > 1
3 to the 21st power / 2 to the 31st power > 1
That is: the 21st power of 3 is greater than the 31st power of 2
=The 10th power of (2 + 1 / 4) multiplied by the 10th power of (3 / 2) / 2
=The 10th power of (1 + 1 / 8) multiplied by (3 / 2)
=9 / 8 times (3 / 2) > 1
2 to the power of 31 (2147483648)
3 to the 21st power (10460353203)
3 to the 21st power
You don't have to work it out
Two numbers that multiply 3 ^ 21 and 2 ^ 31
3^21=3*3^20=3*9^10
2^31=2*2^30=2*8^10
3 > 2,9 ^ 10 > 8 ^ 10
That is, the two numbers of 3 ^ 21 dividends are greater than the two numbers of 2 ^ 31 dividends
So 3 ^ 21 > 2 ^ 31