What is log_{3}(x^2+9x+18)-log_{3}(x+3) ?

The solution to log_{3}(x^2+9x+18)-log_{3}(x+3) is log_{3}(x+6)

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simplify log_{3}(x^2+9x+18)-log_{3}(x+3)

simplify

lo g_{3} (x^{2} + 9 x + 18) - lo g_{3} (x + 3)

lo g_{3} (x + 6)

Solution steps

lo g_{3} (x^{2} + 9 x + 18) - lo g_{3} (x + 3)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} (x^{2} + 9 x + 18) - lo g_{3} (x + 3) = lo g_{3} (\frac{x ^{2} + 9 x + 18}{x + 3})

= lo g_{3} (\frac{x ^{2} + 9 x + 18}{x + 3})

Simplify

\frac{x ^{2} + 9 x + 18}{x + 3} : x + 6

= lo g_{3} (x + 6)

\frac{2}{3} lo g_{10} (\frac{5.96 x ^{1016}}{1 0 ^{4.4}})

lo g_{2} (\frac{x}{500})

ln (\frac{e ^{7}}{9})

4 lo g_{5} (x) + lo g_{5} (y)

ln (cos (x)) + ln (sin (x))

What is log_{3}(x^2+9x+18)-log_{3}(x+3) ?
The solution to log_{3}(x^2+9x+18)-log_{3}(x+3) is log_{3}(x+6)