What is log_{10}(x+5)-log_{10}(x^2+9x+20) ?

The solution to log_{10}(x+5)-log_{10}(x^2+9x+20) is -log_{10}(x+4)

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simplify log_{10}(x+5)-log_{10}(x^2+9x+20)

simplify

lo g_{10} (x + 5) - lo g_{10} (x^{2} + 9 x + 20)

- lo g_{10} (x + 4)

Solution steps

lo g_{10} (x + 5) - lo g_{10} (x^{2} + 9 x + 20)

Apply log rule:

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

lo g_{10} (x + 5) - lo g_{10} (x^{2} + 9 x + 20) = lo g_{10} (\frac{x + 5}{x ^{2} + 9 x + 20})

= lo g_{10} (\frac{x + 5}{x ^{2} + 9 x + 20})

Simplify

\frac{x + 5}{x ^{2} + 9 x + 20} : \frac{1}{x + 4}

= lo g_{10} (\frac{1}{x + 4})

Simplify

\frac{1}{x + 4} : (x + 4)^{- 1}

= lo g_{10} ((x + 4)^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} ((x + 4)^{- 1}) = - 1 \cdot lo g_{10} (x + 4)

= - 1 \cdot lo g_{10} (x + 4)

Apply rule:

1 \cdot a = a

= - lo g_{10} (x + 4)

ln (x^{0.1} \cdot 0.7)

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lo g_{10} (6) + lo g_{10} (8)

ln (\frac{x ^{2}}{( x - 1 ) ^{3}})

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

What is log_{10}(x+5)-log_{10}(x^2+9x+20) ?
The solution to log_{10}(x+5)-log_{10}(x^2+9x+20) is -log_{10}(x+4)