What is log_{9}(k^2-81)-log_{9}(k-9) ?

The solution to log_{9}(k^2-81)-log_{9}(k-9) is log_{9}(k+9)

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simplify log_{9}(k^2-81)-log_{9}(k-9)

simplify

lo g_{9} (k^{2} - 81) - lo g_{9} (k - 9)

lo g_{9} (k + 9)

Solution steps

lo g_{9} (k^{2} - 81) - lo g_{9} (k - 9)

Apply log rule:

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

lo g_{9} (k^{2} - 81) - lo g_{9} (k - 9) = lo g_{9} (\frac{k ^{2} - 81}{k - 9})

= lo g_{9} (\frac{k ^{2} - 81}{k - 9})

Simplify

\frac{k ^{2} - 81}{k - 9} : k + 9

= lo g_{9} (k + 9)

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What is log_{9}(k^2-81)-log_{9}(k-9) ?
The solution to log_{9}(k^2-81)-log_{9}(k-9) is log_{9}(k+9)