What is log_{10}(k^2-100)-log_{10}(k-10) ?

The solution to log_{10}(k^2-100)-log_{10}(k-10) is log_{10}(k+10)

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simplify log_{10}(k^2-100)-log_{10}(k-10)

simplify

lo g_{10} (k^{2} - 100) - lo g_{10} (k - 10)

lo g_{10} (k + 10)

Solution steps

lo g_{10} (k^{2} - 100) - lo g_{10} (k - 10)

Apply log rule:

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

lo g_{10} (k^{2} - 100) - lo g_{10} (k - 10) = lo g_{10} (\frac{k ^{2} - 100}{k - 10})

= lo g_{10} (\frac{k ^{2} - 100}{k - 10})

Simplify

\frac{k ^{2} - 100}{k - 10} : k + 10

= lo g_{10} (k + 10)

ln (\frac{x ^{2} - 1}{x ^{9}})

(- ln (2)) ln^{2} (\frac{- ln ( 2 )}{2})

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

lo g_{2} (\frac{32}{x y ^{2}})

What is log_{10}(k^2-100)-log_{10}(k-10) ?
The solution to log_{10}(k^2-100)-log_{10}(k-10) is log_{10}(k+10)