# A log function

Calculus Level pending

If $$f(x)= \ln{x} (x>0),$$ which of the following statements is true?

a. There is no $$x$$ that satisfies $$\ln{x} = - \frac{1}{x}.$$

b. $$g(x)= {e}^{x}f(x)$$ is an increasing function.

c. If $$0 < a < b ,$$ then $$1-\frac{a}{b} < f(\frac{b}{a}) < \frac{b}{a} -1.$$

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