# How do you evaluate  ln (2x+3)=7?

Mar 10, 2018

$x \approx 546.817$ or $x = \frac{{e}^{7} - 3}{2}$

#### Explanation:

Remember, anytime you see ln, it is always equal to
$\log e$ (the e is a subscript). You work with them the same way as you would any other log.
Problem:
$\ln \left(2 x + 3\right) = 7$
Step 1: take $\log e$ of both sides.
$\ln \left(2 x + 3\right) = \ln \left({e}^{7}\right)$
Step 2: Since the logs have the same bases, make the $\left(2 x + 3\right) = \left({e}^{7}\right)$ equal to each other
Step 3: Solve so the x is on the left side by itself:
$x = \frac{{e}^{7} - 3}{2}$
Step 4: if you need the decimal form, just plug in 2.718281828 (Euler's number) for e and solve.
x=(2.718281828 ^7 -3)/2 => x~~546.817