Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 452: 15

$a)$ $(0,1)$ $b)$ $ x \in (\ln5,+\infty)$

$a$- The natural logarithm function is negative on $(0,1)$ so the solution to the first inequality is: $$(0,1)$$ $b$- $$e^{x} \gt 5$$ $$\ln(e^{x}) \gt \ln(5)$$ $$x \gt \ln(5)$$ $$ x \in (\ln5,+\infty)$$