Question

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Answer 1

\[g(x)= \log_{1/e}(x) \]

Answer 2

ff(x) and g(x) are symmetric about the x-axis, so area is:
\[2 \int\limits_1^e \ln(x) dx\]

Answer 3

Have you tried graphing these two curves, to determine whether they intersect or not? Doing this might help you determine the limits of integration as well. The upper limit is x=e (given). Think about how you might determine the lower limit of integration.

Note: You haven't posted the answer choices yet.

Answer 4

\(g(x)= \log_{1/e}(x)\)

base shift it \( \log_{1/e}(x) = \dfrac{log_e x}{\log_e (1/e)} = \dfrac{\ln x}{-\ln e } = - \ln x \)

so you just do the top one times 2! i reckon!

which means \(2~ \int\limits_{1}^{e} ~ \ln(x) ~ dx\)