How do you condense $ln 3 - 2 ln (9 + 3)$ $ln 3 − 2 ln(9 + 3)$ ?

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Answer 1 · 2016-06-27T21:13:41

$ln [\frac{1}{48}]$ $ln[1/48]$

Simplify the bracket:

$ln 3 - 2 ln (9 + 3) = ln 3 - 2 ln (12)$ $ln3 - 2lncolor(blue)((9+3)) = ln3 - 2lncolor(blue)((12))$

If you are subtracting the logs, you must have been dividing the numbers.

Use the power rule first:

$ln 3 - 2 ln (12) = ln 3 - {ln (12)}^{2}$ $ln3 - color(red)2ln(12) = ln3 - ln(12)^color(red)2$

Write as a log of a single number:

$= ln [\frac{3}{{(12)}^{2}}]$ $=ln[3/(12)^2]$

$= ln (\frac{3}{144}) = ln [\frac{1}{48}]$ $= ln(3/144) = ln[1/48]$

How do you condense ln 3 − 2 ln(9 + 3) ln3−2ln(9+3) ln 3 − 2 ln(9 + 3) ?