Solve for x 6e^(-1.4x)=21

Problem

6*e(−1.4*x)=21

Solution

1. Isolate the exponential term by dividing both sides of the equation by 6

e(−1.4*x)=21/6

2. Simplify the fraction on the right side by dividing the numerator and denominator by their greatest common divisor, 3

e(−1.4*x)=3.5

3. Apply the natural logarithm to both sides of the equation to undo the exponential function.

ln(e(−1.4*x))=ln(3.5)

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

−1.4*x=ln(3.5)

5. Solve for x by dividing both sides by −1.4

x=ln(3.5)/(−1.4)

6. Calculate the numerical value using a calculator.

x≈−0.8948

Final Answer

x=ln(3.5)/(−1.4)≈−0.8948

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