What is log_{9}(x^2+13x+40)-log_{9}(x+8) ?

The solution to log_{9}(x^2+13x+40)-log_{9}(x+8) is log_{9}(x+5)

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simplify log_{9}(x^2+13x+40)-log_{9}(x+8)

simplify

lo g_{9} (x^{2} + 13 x + 40) - lo g_{9} (x + 8)

lo g_{9} (x + 5)

Solution steps

lo g_{9} (x^{2} + 13 x + 40) - lo g_{9} (x + 8)

Apply log rule:

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

lo g_{9} (x^{2} + 13 x + 40) - lo g_{9} (x + 8) = lo g_{9} (\frac{x ^{2} + 13 x + 40}{x + 8})

= lo g_{9} (\frac{x ^{2} + 13 x + 40}{x + 8})

Simplify

\frac{x ^{2} + 13 x + 40}{x + 8} : x + 5

= lo g_{9} (x + 5)

3.8 + lo g_{10} (\frac{0.2 - 0.02}{0.5 + 0.02})

lo g_{2} (\frac{8 a ^{2} 2 - b}{c ( b + 3 ) ^{2}})

lo g_{10} (\frac{x ^{2} y ^{3}}{z ^{4}})

lo g_{2} (\frac{z}{8})

ln (\frac{7}{6 x ^{6} y})

What is log_{9}(x^2+13x+40)-log_{9}(x+8) ?
The solution to log_{9}(x^2+13x+40)-log_{9}(x+8) is log_{9}(x+5)