Question

What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 1?

Answer 1

$ln(x + 6) - ln(2x - 1) = 1$
$ln(\frac{x + 6}{2x - 1}) = 1$
$\frac{x + 6}{2x - 1} = e^{1}$
$\frac{x + 6}{2x - 1} \approx 2.72$
$2x - 1(\frac{x + 6}{2x - 1}) = 2.72(2x - 1)$
$x + 6 = 2.72(2x) - 2.72(1)$
$x + 6 = 5.44x - 2.72$
$6 = 4.44x - 2.72$
$8.72 = 4.44x$
$\frac{8.72}{4.44} = \frac{4.44x}{-3.28}$
$1.97 \approx x$

The answer is D.