Answer
$8 \ln (4)-16+2e$
Work Step by Step
Here, we have: $y=\ln (x)$ and $y=2 -\ln x$
Suppose that $y=y \implies \ln x=2-\ln x$
or, $2 \ln x =2 \implies x=e$
Here, the area can be expressed as: $A=\int_{e}^{4} [\ln x-(2-\ln x)] \ dx$
or, $=\int_{e}^{4} (2\ln x-2) \ dx$
or, $=(2 x\ln x-2x-2x)_e^4$
or, $=(2 x\ln x-4x)_e^4$
or, $=[2 (4)\ln (4)-4(4))-[2 e \ln e -4(e)]$
Therefore, the required area is: $Area=8 \ln (4)-16+2e$
