# How it has to be the argument of logarithmic function?Need example, please!

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

x>0

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.