Remembering that exponential functions and logarithms (with the same base) are inverses, decide if each of the following expressions will simplify to just $x\text{.}$

1. $\log_{10}(x)\cdot 10^x = x\text{?}$
   Answer: ? true false
2. $\log_{10}\left(10^x\right) = x\text{?}$
   Answer: ? true false
3. $e^{\ln(x)} = x\text{?}$
   Answer: ? true false
4. $\ln\left(e^x\right)$
   Answer: ? true false