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Solve for the exact value of x. 5ln(8x+6)-12=3 Answer:

Solve for the exact value of x x .\newline5ln⁡(8x+6)−12=3 5 \ln (8 x+6)-12=3 \newlineAnswer:

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Full solution

Q. Solve for the exact value of x x .\newline5ln⁡(8x+6)−12=3 5 \ln (8 x+6)-12=3 \newlineAnswer:
  1. Isolate natural logarithm term: Isolate the natural logarithm term.\newlineWe start by adding 1212 to both sides of the equation to isolate the term with the natural logarithm.\newline5ln⁡(8x+6)−12+12=3+125\ln(8x+6) - 12 + 12 = 3 + 12\newline5ln⁡(8x+6)=155\ln(8x+6) = 15
  2. Divide sides to solve: Divide both sides by 55 to solve for the natural logarithm of the expression.\newline5ln⁡(8x+6)5=155 \frac{5\ln(8x+6)}{5} = \frac{15}{5} \newlineln⁡(8x+6)=3 \ln(8x+6) = 3
  3. Exponentiate to remove logarithm: Exponentiate both sides to remove the natural logarithm.\newlineeln⁡(8x+6)=e3e^{\ln(8x+6)} = e^3\newline8x+6=e38x+6 = e^3
  4. Subtract to solve for 8x8x: Subtract 66 from both sides to solve for 8x8x.8x+6−6=e3−68x + 6 - 6 = e^3 - 68x=e3−68x = e^3 - 6
  5. Divide to solve for x: Divide both sides by 88 to solve for x.\newline8x8=e3−68\frac{8x}{8} = \frac{e^3 - 6}{8}\newlinex=e3−68x = \frac{e^3 - 6}{8}

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