How do you simplify #ln(e^(-2x)) / x#?

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Answer 1 · 2016-08-20T21:00:14

This simplifies to #-2#

Start of by rewriting as follows

#ln(1/e^(2x))/x#

Using properties of logarithms we can rewrite the numerator

#(ln|1|-ln|e^(2x)|)/x#

Remember #ln|1|=0#

#(0-ln|e^(2x)|)/x#

Now rewrite the numerator again

#(-2xln|e|)/x#

Remember #ln|e|=1#

#(-2x)/x=-2#