How it has to be the argument of logarithmic function?Need example, please!
The argument of logarithmic function has to be positive, for the logarithmic function to exist.
We know that the domain of logarithmic function is (0 ; +infinite) and the codomain is R (real number set).
f(x) = log x
The argument could be the variable itself, or an expression, like in this case:
log (x^2 -6x + 5)
For the logarithm function to exist, we'll impose the constraint to argument:
x^2 -6x + 5 > 0
We'll find out the zeroes of the argument first:
x1 = 1 and x2 = 5
The argument is positive over the ranges:
[(-infinite 1)U(5;+infinite)] intersected (0;+infinite) = (0;infinite)
Of course, there are cases when the argument is positive for any real value of x, like in the case x^2 + x + 1.
x^2+x+1>0 for any value of x.
Conclusion: the argument of logarithmic function has to be positive, for the logarithmic function to exist.