# the range of the function t→lnt defined for all positive numbers in?

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The domain of the natural logarithm of t, `lnt` , is the positive real numbers.

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**The range of the natural logarithm is all real numbers.**

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From a calculus perspective, the natural logarithm is a continuous function (everywhere continuous on its domain) which is monotonically increasing (if a>b, then f(a)>f(b) for all a,b in the domain) since the first derivative is always positive.

Note that the mapping `t->lnt` is equivalent to `f(t)=lnt` .

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