What is log_{5}(a^2+10a+9)-log_{5}(a+9)+2 ?

The solution to log_{5}(a^2+10a+9)-log_{5}(a+9)+2 is log_{5}(a+1)+2

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simplify log_{5}(a^2+10a+9)-log_{5}(a+9)+2

simplify

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) + 2

lo g_{5} (a + 1) + 2

Solution steps

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) + 2

Apply log rule:

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

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) = lo g_{5} (\frac{a ^{2} + 10 a + 9}{a + 9})

= lo g_{5} (\frac{a ^{2} + 10 a + 9}{a + 9}) + 2

Simplify

\frac{a ^{2} + 10 a + 9}{a + 9} : a + 1

= lo g_{5} (a + 1) + 2

lo g_{10} (7.2) - lo g_{10} (6.7)

ln (12) - ln (5)

2 ln (5 y) + \frac{1}{x}

- \frac{3}{9} lo g_{2} (\frac{3}{9}) - \frac{6}{9} lo g_{2} (\frac{6}{9})

10 ln (4 x) - ln^{2} (4 x)

What is log_{5}(a^2+10a+9)-log_{5}(a+9)+2 ?
The solution to log_{5}(a^2+10a+9)-log_{5}(a+9)+2 is log_{5}(a+1)+2