Approximate the solution to $\ln ( x + 3 ) - \ln x = 1$ . Round to 3 decimal places.
A)-0.632
B)0.250
C)1.746
D)2.718
E)0.333

Question

Quizplus · Accepted Answer

Using properties of logarithms, the equation can be rewritten as $\ln\left(\frac{x + 3}{x}\right) = 1$. Exponentiating both sides gives $\frac{x + 3}{x} = e^1 = e$. Solving for $x$, we get $x + 3 = ex$, leading to $x(e - 1) = 3$, and thus $x = \frac{3}{e - 1}$. Calculating this gives approximately $x = 1.746$.

Approximate the Solution To ln⁡(x+3)−ln⁡x=1\ln ( x + 3 ) - \ln x = 1ln(x+3)−lnx=1

Approximate the Solution To $\ln ( x + 3 ) - \ln x = 1$