Solve the following log equation to find the solutions expressed in an exact form.

$$9\log_x e = \ln x$$

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\( 9\log_x e = \ln x \)

Changing base

\( 9 \frac{ \ln e}{ \ln x} = \ln x \)

\( 9 = (\ln x)^2 \)

\( ln x = 3 \; \text{and} -3 \)

\( x = e^3 \; \text{and} \; e^{-3} \)

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