How do you solve #e^ { x + 4} = \frac { 1} { e ^ { 6} }#?

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Answer 1 · 2017-04-24T15:51:48

#x=-10#

Ideally, we want it in the form #e^(x+4)=e^"some number"#. We have to rewrite #1/e^6# somehow.

Luckily, we can change the sign of the exponent in order to write it in the numerator:

#e^(x+4)=1/(e^6)#

#e^(x+4)=e^(-6)#

Now we can compare exponenents:

#x+4=-6#

Solve for #x#

#x=-10#