We have to expand: ln(3e^(2x)).

Here we make use of the relations log a^n = n* log a and log ab = log a + log b

ln(3e^(2x))

=> ln 3 + ln e^2x

=> ln 3 + 2x*ln e

ln e = 1

=> ln 3 + 2x

**The required expansion is ln 3 + 2x**

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