Solve ln(4x+3) - ln(x²-8) = 2: Finding the Value of x

The natural logarithm $\ln(x)$ is only defined for positive real numbers. If you try to take $\ln(-5)$ or $\ln(0)$, it's mathematically undefined in the real number system.

After using the quadratic formula, you'll get two potential solutions. Check both by substituting into the domain restrictions. Only keep solutions where both $4x+3 > 0$ and $x^2-8 > 0$.

$e^2 \approx 7.389$ where e is Euler's number (approximately 2.718). You can use this decimal approximation in your calculations, but keep more precision until your final answer.

While you could exponentiate each side separately, using $\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ simplifies the problem significantly. It reduces two logarithms to one, making the algebra much cleaner.

The exact answer involves $e^2$ which is irrational. We use decimal approximations to match the multiple choice format. The exact form would be more complex but equivalent.

If your solution makes $x^2-8 = 0$ (so $x = \pm 2\sqrt{2}$), that solution is invalid because it creates division by zero in the original equation. Always exclude such values.