What is log_{10}(x^2-9)-log_{10}(x^2+6x+9) ?

The solution to log_{10}(x^2-9)-log_{10}(x^2+6x+9) is log_{10}((x-3)/(x+3))

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simplify log_{10}(x^2-9)-log_{10}(x^2+6x+9)

simplify

lo g_{10} (x^{2} - 9) - lo g_{10} (x^{2} + 6 x + 9)

lo g_{10} (\frac{x - 3}{x + 3})

Solution steps

lo g_{10} (x^{2} - 9) - lo g_{10} (x^{2} + 6 x + 9)

Apply log rule:

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

lo g_{10} (x^{2} - 9) - lo g_{10} (x^{2} + 6 x + 9) = lo g_{10} (\frac{x ^{2} - 9}{x ^{2} + 6 x + 9})

= lo g_{10} (\frac{x ^{2} - 9}{x ^{2} + 6 x + 9})

Simplify

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

= lo g_{10} (\frac{x - 3}{x + 3})

\frac{144}{81}

2 \cdot 19

2 \cdot 4 x

5 (5 x^{2} - 2 x + 1)^{2} - 2 (5 x^{2} - 2 x + 1) + 1

\frac{8 a ^{4} b ^{6}}{2 ( a ^{5} b ) ^{2}}

What is log_{10}(x^2-9)-log_{10}(x^2+6x+9) ?
The solution to log_{10}(x^2-9)-log_{10}(x^2+6x+9) is log_{10}((x-3)/(x+3))