What is log^2_{3}(x+2)-log_{3}(x^2+4x+4) ?

The solution to log^2_{3}(x+2)-log_{3}(x^2+4x+4) is log_{3}(x+2)^2

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simplify log^2_{3}(x+2)-log_{3}(x^2+4x+4)

simplify

lo g_{3}^{2} (x + 2) - lo g_{3} (x^{2} + 4 x + 4)

lo g_{3} (x + 2)^{2}

Solution steps

lo g_{3}^{2} (x + 2) - lo g_{3} (x^{2} + 4 x + 4)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{3}^{2} (x + 2) - lo g_{3} (x^{2} + 4 x + 4) = lo g_{3}^{2} (\frac{x + 2}{x ^{2} + 4 x + 4})

= lo g_{3}^{2} (\frac{x + 2}{x ^{2} + 4 x + 4})

Simplify

\frac{x + 2}{x ^{2} + 4 x + 4} : \frac{1}{x + 2}

= lo g_{3}^{2} (\frac{1}{x + 2})

Simplify

lo g_{3} (\frac{1}{x + 2}) : - lo g_{3} (x + 2)

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

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= lo g_{3} (x + 2)^{2}

lo g_{10} (27) - lo g_{10} (9)

2 lo g_{10} (3) - 3 lo g_{10} (2)

ln (5) + ln (2)

1 - lo g_{4} (m - 1) - lo g_{4} (m + 1)

lo g_{2} (3) - 3 lo g_{2} (x) + \frac{1}{2} lo g_{2} (x + 1)

What is log^2_{3}(x+2)-log_{3}(x^2+4x+4) ?
The solution to log^2_{3}(x+2)-log_{3}(x^2+4x+4) is log_{3}(x+2)^2