How do you solve ln x - ln 4 = 7?

Oct 28, 2015

$x = 4 {e}^{7}$
You must see the explanation!

Explanation:

You need to know that :
log to base 10 of $x = 7$ is ${\log}_{10} \left(x\right) = 7 \to {10}^{7} = x$
log to base $e$ of $x = 7$ is ${\log}_{e} \left(x\right) = 7 \to {e}^{7} = x$
log to base $e$ of $x$ is normally written as $\ln \left(x\right)$

Addition of loges reflects multiplication of the source numbers.
Subtraction of logs reflects division of the source numbers.
This is so because you are dealing with indices (powers).

This is stating that:

$\ln \left(x\right) - \ln \left(4\right) = \ln \left(\frac{x}{4}\right) = 7$

so ${e}^{7} = \frac{x}{4}$

so $x = 4 {e}^{7}$