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

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Answer 1 · 2017-04-24T15:51:48

$x = - 10$ $x=-10$

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

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

$e^{x + 4} = \frac{1}{e^{6}}$ $e^(x+4)=1/(e^6)$

$e^{x + 4} = e^{- 6}$ $e^(x+4)=e^(-6)$

Now we can compare exponenents:

$x + 4 = - 6$ $x+4=-6$

Solve for $x$ $x$

$x = - 10$ $x=-10$

How do you solve e^ { x + 4} = \frac { 1} { e ^ { 6} }ex+4=1e6e^ { x + 4} = \frac { 1} { e ^ { 6} }?