The approximate interval of the solution of the equation x = 3-lgx is? The answer is between "2.3"

The approximate interval of the solution of the equation x = 3-lgx is? The answer is between "2.3"

The equation can be changed to lgx = x + 3, which is regarded as the intersection of y = lgx and y = x + 3
Because one of the two functions increases monotonically and the other decreases monotonically, the intersection point is unique. You only need to substitute a few integers to compare the size (with a calculator) to get the approximate interval

A solvable interval (a, b) of the equation (lgx) + x = 4 is obtained so that B-A is less than or equal to 1

When x = 3, lgx + 3 < 4,
When x = 4, lgx + 4 > 4,
So the equation must have a solution in (3,4)
(lgx is based on 10)

The interval of solution of equation lgx-1 / x = 0 is

lgx=1/x
xlgx =1=lg10
x^x=10
∵3^3=9,4^4=256
Ψ X in (3,4)

The solution set of the equation x ^ (lgx + 1) - 100 = 0 is

X ^ (lgx + 1) - 100 = 0
X ^ (lgx + 1) = 100, take the common logarithm on both sides, get lgx + 1 = 2 / lgx, the solution, x = 10 or x = 1 / 100