How do you solve ln(2x+3)-4=15?

Sep 27, 2015

$x = \frac{{e}^{19} - 3}{2}$

Explanation:

$\ln \left(2 x + 3\right) - 4 = 15$
$\ln \left(2 x + 3\right) = 19$

Take the exponential of both sides, then solve using algebra

$2 x + 3 = {e}^{19}$
$2 x = {e}^{19} - 3$
$x = \frac{{e}^{19} - 3}{2}$

Double checking this value gives the right answer, and when x is that value we aren't taking the logarithm of a negative or a null number so all's okay.