Errors in CAS and Geometry

[Jan 11]

(10-14-2022 08:21 PM)klesl Wrote:  for x=2.0001
x^2-30=-26
ln(x-2)=-9.21
-26 doesn't equal to -9.21

A little bit mathematics:
ln(x-2), where x is close to 2 can be rewritten as ln(d), d=x-2=1/10^n=ln(1)-ln(1/10^n)=0-ln(1)-ln(10^n)=0-0-n×ln(10)=-2.303n,
n is number of decimal places (order), e.g. x=2.0001 so n=4 and ln(2.0001-2)=-4*2.303=-9.21
Based on the calculation above the order is between 11 (-25.328) and 12 (-27.631) and with respect to the order are whole number only (you cannot have 11.5 decimal places) this solution clearly doesn't exists

There is a number that is a solution to this equation, and it is a number very close to 2, but not 2, obviously greater than 2 (that is, the domain of the logarithm). Well, let's count
(x ^ 2 - 30) I for x = 2.00000000001, f (x) = -26
LN (x -2) I for x = 2.00000000001. f (x) = -25.329.
So you can take the number x = 2.00000000001 as the second root of this equation.