Solve for x 4e^(x+1)=5

Problem

4*e(x+1)=5

Solution

1. Isolate the exponential term by dividing both sides of the equation by 4

e(x+1)=5/4

2. Apply the natural logarithm ln() to both sides to undo the exponential function.

ln(e(x+1))=ln(5/4)

3. Simplify the left side using the property ln(eu)=u

x+1=ln(5/4)

4. Solve for x by subtracting 1 from both sides.

x=ln(5/4)−1

Final Answer

x=ln(5/4)−1

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