Solve for x 119/(e^(6x)-14)=7

Problem

119/(e(6*x)−14)=7

Solution

1. Multiply both sides by the denominator e(6*x)−14 to clear the fraction.

119=7*(e(6*x)−14)

2. Divide both sides by 7 to isolate the term containing the exponential.

119/7=e(6*x)−14

17=e(6*x)−14

3. Add 14 to both sides to isolate the exponential term e(6*x)

17+14=e(6*x)

31=e(6*x)

4. Apply the natural logarithm ln() to both sides to solve for the exponent.

ln(31)=ln(e(6*x))

ln(31)=6*x

5. Divide by 6 to solve for x

x=ln(31)/6

Final Answer

119/(e(6*x)−14)=7⇒x=ln(31)/6

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