# How do you solve -7 + ln 2x =4?

$x = \frac{1}{2} \cdot {e}^{11}$

#### Explanation:

from the given $- 7 + \ln 2 x = 4$
transpose -7 to the right of the equation

$\ln 2 x = 4 + 7$

simplify

$\ln 2 x = 11$

this is also

${\ln}_{e} 2 x = 11$

convert to exponential form

${e}^{11} = 2 x$

divide both sides of the equation by 2

$x = \frac{1}{2} \cdot {e}^{11}$

Do the checking at $x = \frac{1}{2} \cdot {e}^{11}$ using the original equation

$- 7 + \ln 2 x = 4$
$- 7 + \ln 2 \left(\frac{1}{2} \cdot {e}^{11}\right) = 4$
$- 7 + \ln {e}^{11} = 4$
$- 7 + 11 = 4$
$4 = 4$ correct !!!

God bless you ...