#### Answer

5.0096

#### Work Step by Step

We know that logarithms with base $e$ are natural logarithms, and $ln(x)$ can be written as $log_{e}x$.
Therefore, $ln(7.46\times e^{3})=log_{e}(7.46\times e^{3})$.
We know that for all positive numbers $a$ (where $a\ne1$), and all positive numbers $x$, $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{e}(7.46\times e^{3})\approx5.0096$, because $e^{5.0096}\approx e^{(7.46\times e^{3})}$.