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

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Answer 1 · 2015-07-08T03:05:38

use of logarithm property and then antilog

remember

$ln a - ln b = ln (\frac{a}{b})$ $lna-lnb=ln(a/b)$

so applying it here we see that

$ln x - ln (x - 3) = ln 5$ $lnx-ln(x-3)=ln5$ can be rewritten as

$ln (\frac{x}{x - 3}) = ln 5$ $ln(x/(x-3))=ln5$

now taking antilog on both sides we get

$a n t i ln (ln (\frac{x}{x - 3})) = a n t i ln (ln 5)$ $antiln(ln(x/(x-3)))=antiln(ln5)$

$\frac{x}{x - 3} = 5$ $x/(x-3)=5$

solving the equation reveals

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

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

How do you solve lnx−ln(x−3)=ln5?ln x - ln (x-3) = ln 5??