How do you simplify $ln (3 x^{2} - 9 x) + ln (\frac{1}{3 x})$ $ln(3x^2-9x)+ln(1/(3x))$ ?

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Answer 1 · 2016-05-03T01:59:06

$log (x - 3)$ $log (x-3)$ , x > 3.

Use log $a b c = log a + log b + log c and log (\frac{1}{d}) = - log d$ $abc = log a + log b + log c and log(1/d) = - log d$ ,

$log (3 x^{2} - 9 x) + log (\frac{1}{3 x})$ $log (3x^2-9x)+log(1/(3x))$

$= log ((3) (x) (x - 3)) - log ((3) (x))$ $=log((3)(x)(x-3))-log( (3)(x))$

$= log 3 + log x + log (x - 3) - log 3 - log x$ $=log 3+log x + log(x-3)-log 3 - log x$

$= log (x - 3)$ $=log (x-3)$ , with x > 3..

How do you simplify ln(3x^2-9x)+ln(1/(3x))ln(3x2−9x)+ln(13x)ln(3x^2-9x)+ln(1/(3x))?