Question

How do you solve `-2e ^ { 2x + 8} - 3= 23`?

Answer 1

There is no solution.

Explanation:

Start to solve for `x` by first isolating `e^(2x+8)`. Add `3` to both sides of the equation:

`-2e^(2x+8)=26`

Diving by `-2`:

`e^(2x+8)=-13`

We have an issue. An exponential function like `e^(2x+8)` must be positive.

We can also see this issue if we try to solve for `2x+8` by taking the natural logarithm of both sides:

`2x+8=ln(-13)`

It's impossible to take the logarithm of a negative number for the same reason as above: there's no way an exponent of a positive number, like `e`, can result in a negative number.

Therefore this equation has no solutions.

Graphed is `e^(2x+8)`. Notice how it is always positive:

graph{e^(2x+8) [-19.82, 12.22, -4.17, 11.85]}