# How do you solve ln x - ln (x-3) = ln 5??

##### 1 Answer
Jul 8, 2015

use of logarithm property and then antilog

#### Explanation:

remember

$\ln a - \ln b = \ln \left(\frac{a}{b}\right)$

so applying it here we see that

$\ln x - \ln \left(x - 3\right) = \ln 5$ can be rewritten as

$\ln \left(\frac{x}{x - 3}\right) = \ln 5$

now taking antilog on both sides we get

$a n t i \ln \left(\ln \left(\frac{x}{x - 3}\right)\right) = a n t i \ln \left(\ln 5\right)$

$\frac{x}{x - 3} = 5$

solving the equation reveals

$x = \frac{15}{4}$

please feel free to comment if you find any mistake
Cheerio!