Solve for x e^(3x)=e^(2-x)

Problem

e(3*x)=e(2−x)

Solution

1. Apply the property of equality for exponential functions. Since the bases on both sides are the same (e, their exponents must be equal.

3*x=2−x

2. Isolate the variable by adding x to both sides of the equation to collect all x terms on the left.

4*x=2

3. Solve for x by dividing both sides by 4

x=2/4

4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2

x=1/2

Final Answer

x=1/2

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