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Solve for the exact value of x. 4ln(5x-6)+10=18 Answer:

Solve for the exact value of x x .\newline4ln⁡(5x−6)+10=18 4 \ln (5 x-6)+10=18 \newlineAnswer:

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Full solution

Q. Solve for the exact value of x x .\newline4ln⁡(5x−6)+10=18 4 \ln (5 x-6)+10=18 \newlineAnswer:
  1. Isolate natural logarithm term: Isolate the natural logarithm term by subtracting 1010 from both sides of the equation.\newline4ln⁡(5x−6)+10−10=18−104\ln(5x-6) + 10 - 10 = 18 - 10\newline4ln⁡(5x−6)=84\ln(5x-6) = 8
  2. Divide by 44: Divide both sides of the equation by 44 to solve for the natural logarithm of (5x−6)(5x-6).4ln⁡(5x−6)4=84\frac{4\ln(5x-6)}{4} = \frac{8}{4}ln⁡(5x−6)=2\ln(5x-6) = 2
  3. Exponentiate to remove ln: Exponentiate both sides of the equation to remove the natural logarithm, using the property eln⁡(x)=xe^{\ln(x)} = x.\newlineeln⁡(5x−6)=e2e^{\ln(5x-6)} = e^2\newline5x−6=e25x - 6 = e^2
  4. Add 66 to isolate x: Add 66 to both sides of the equation to isolate the term with xx.5x−6+6=e2+65x - 6 + 6 = e^2 + 65x=e2+65x = e^2 + 6
  5. Divide by 55 to solve xx: Divide both sides of the equation by 55 to solve for xx.5x5=(e2+6)5\frac{5x}{5} = \frac{(e^2 + 6)}{5}x=(e2+6)5x = \frac{(e^2 + 6)}{5}

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