Answer:
The rewritten equation is: ![x = \ln{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cln%7B4%7D)
Step-by-step explanation:
The inverse operation of the exponential is the natural logarithm,
, and the following property is used to solve this question:
![\ln{e^x} = x](https://tex.z-dn.net/?f=%5Cln%7Be%5Ex%7D%20%3D%20x)
In this question, we have that:
![4e^x = 16](https://tex.z-dn.net/?f=4e%5Ex%20%3D%2016)
![e^x = \frac{16}{4}](https://tex.z-dn.net/?f=e%5Ex%20%3D%20%5Cfrac%7B16%7D%7B4%7D)
![e^x = 4](https://tex.z-dn.net/?f=e%5Ex%20%3D%204)
Applying the natural logarithm to both sides:
![\ln{e^x} = \ln{4}](https://tex.z-dn.net/?f=%5Cln%7Be%5Ex%7D%20%3D%20%5Cln%7B4%7D)
![x = \ln{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cln%7B4%7D)
The rewritten equation is: ![x = \ln{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cln%7B4%7D)