Question

Solve for x: e^ln5 = x ln1 - lne = x ln6 + ln(x) - ln(2) =3

Answer 1

$e^{ln(5)} = x$
$5 = x$

$ln(1) - ln(e) = x$
$0 + 1 = x$
$1 = x$

$ln(6) + ln(x) - ln(2) = 3$
$ln(6) - ln(2) + ln(x) = 3$
$\frac{ln(6)}{ln(2)} + ln(x) = 3$
$\frac{ln(3) + ln(2)}{ln(2)} + ln(x) = 3$
$\frac{ln(3)}{ln(2)} + 1 + ln(x) = 3$
$\frac{ln(3)}{ln(2)} + ln(x) = 2$
$\frac{ln(3x)}{ln(2)} = 2$
$\frac{3x}{2} = e^{2}$
$\frac{3x}{2} \approx 7.39$
$3x = 14.78$
$x \approx 4.926$