The area bounded by the curve $y = \log x, y = 0$ and $x = e$, is

The area bounded by the curve $y = \log x$, $y = 0$, and $x = e$ needs to be found.

The curve $y = \log x$ crosses the x-axis when $\log x = 0$, which occurs at $x = 1$ since $\log 1 = 0$.

The region extends from $x = 1$ to $x = e$.

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The area is given by:

Area $= \int_{1}^{e} \log x \, dx$

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Using the standard integration formula:

$\int \log x \, dx = x \log x - x + C$

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Applying the limits:

Area $= [x \log x - x]_{1}^{e}$

At $x = e$:

$e \cdot \log e - e$

$= e \cdot 1 - e$

$= 0$

At $x = 1$:

$1 \cdot \log 1 - 1$

$= 1 \cdot 0 - 1$

$= -1$

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Area $= 0 - (-1)$

$= 1$

Therefore, the area bounded by the curve is $1$ square unit.