Solve the given equation for $$ x $$ $$ e^{2 x+4}-e=0 $$ $$ x=\square $$ (Simplify your answer. Type a fraction or an integer. Use a comma to separate answers as needed.)

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UpStudy AI · Accepted Answer

To solve the equation $$ e^{2x + 4} - e = 0 $$:

1. Start by isolating the exponential term:
   $$
   e^{2x + 4} = e
   $$

2. Recognize that $$ e^k = e^1 $$ implies $$ k = 1 $$ because the exponential function is one-to-one:
   $$
   2x + 4 = 1
   $$

3. Solve for $$ x $$:
   $$
   2x = 1 - 4 \
   2x = -3 \
   x = -\frac{3}{2}
   $$

**Answer:** 
$$-\frac{3}{2}$$
$$ x = -\frac{3}{2} $$

Solve the given equation for

(Simplify your answer. Type a fraction or an integer. Use a comma to separate answers as needed.)

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Solve the given equation for (Simplify your answer. Type a fraction or an integer. Use a comma to separate answers as needed.)