X ^ (lgx + 1) - 100 = 0 each step includes the variant in detail

X ^ (lgx + 1) - 100 = 0 each step includes the variant in detail

x^(lgx+1) -100=0
x^(lgx+1) =100
Take logarithm on both sides at the same time
lg[x^(lgx+1)] =lg100
(lgx+1)lgx=2
(lgx)²+lgx-2=0
(lgx-1)(lgx+2)=0
Lgx = 1 or lgx = - 2
X = 10 or x = 0.01

When x > 0 and X ≠ 1, lgx + 1 / lgx ≥ 2, why is it wrong

If 0

The interval of solution of equation lgx − 1x = 0 is ()
A. （0，1）B. （1，2）C. （2，3）D. [1，4]

Let f (x) = 1 x-lgx, then f (1) = 1-0 ＞ 0, f (2) = 12-lg2 ＞ 0, f (3) = 13-lg3 ＜ 0, f (4) = 14-lg4 ＜ 0. The equation 1 x-lgx = 0 must have roots in the interval (2,3), so choose C

X > 1, Y > 1, lgx + lgY = 4, find the maximum value of lgxlgy

x＞1,y＞1
lgx >0 lgy>0
The rest is the mean inequality
The maximum is 4