How do you simplify $ln 3 − 2 ln 9 + ln 18$ ?

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Answer 1 · 2015-09-01T23:29:31

$ln 3 - 2 ln 9 + ln 18 = ln (2/3) = ln 2 - ln 3$

Use: $color(white)(XX)ln a + ln b = ln (ab)$

and: $color(white)(XX)ln a - ln b = ln (a/b)$

to simplify:

$ln 3 - 2 ln 9 + ln 18$

$=ln 3 + ln 18 - ln 9^2$

$=ln (3*18) - ln 81$

$=ln 54 - ln 81$

$=ln (54/81)$

$=ln (2/3)$

$=ln 2 - ln 3$

How do you simplify ln 3 − 2 ln 9 + ln 18 ln 3 − 2 ln 9 + ln 18 ?