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Solve for the exact value of x. 4ln(6x-4)+7=15 Answer:

Solve for the exact value of x x .\newline4ln⁡(6x−4)+7=15 4 \ln (6 x-4)+7=15 \newlineAnswer:

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Full solution

Q. Solve for the exact value of x x .\newline4ln⁡(6x−4)+7=15 4 \ln (6 x-4)+7=15 \newlineAnswer:
  1. Subtract to isolate natural logarithm: Isolate the natural logarithm term by subtracting 77 from both sides of the equation.\newline4ln⁡(6x−4)+7−7=15−74\ln(6x-4) + 7 - 7 = 15 - 7
  2. Simplify by subtraction: Simplify the equation by performing the subtraction. \newline4ln⁡(6x−4)=84\ln(6x-4) = 8
  3. Divide to isolate logarithm: Divide both sides of the equation by 44 to isolate the natural logarithm.\newline4ln⁡(6x−4)4=84\frac{4\ln(6x-4)}{4} = \frac{8}{4}
  4. Simplify by division: Simplify the equation by performing the division.\newlineln⁡(6x−4)=2\ln(6x-4) = 2
  5. Exponentiate to remove logarithm: Exponentiate both sides of the equation to remove the natural logarithm, using the property eln⁡(x)=xe^{\ln(x)} = x. \newlineeln⁡(6x−4)=e2e^{\ln(6x-4)} = e^2
  6. Simplify using logarithm property: Simplify the left side of the equation using the property of logarithms. 6x−4=e26x - 4 = e^2
  7. Addition to isolate x term: Add 44 to both sides of the equation to isolate the term with xx.\newline6x−4+4=e2+46x - 4 + 4 = e^2 + 4
  8. Simplify by addition: Simplify the equation by performing the addition. 6x=e2+46x = e^2 + 4
  9. Divide to solve for xx: Divide both sides of the equation by 66 to solve for xx.x=e2+46x = \frac{e^2 + 4}{6}

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