What is log_{6}(k^2-36)-log_{6}(k-6) ?

The solution to log_{6}(k^2-36)-log_{6}(k-6) is log_{6}(k+6)

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simplify log_{6}(k^2-36)-log_{6}(k-6)

simplify

lo g_{6} (k^{2} - 36) - lo g_{6} (k - 6)

lo g_{6} (k + 6)

Solution steps

lo g_{6} (k^{2} - 36) - lo g_{6} (k - 6)

Apply log rule:

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

lo g_{6} (k^{2} - 36) - lo g_{6} (k - 6) = lo g_{6} (\frac{k ^{2} - 36}{k - 6})

= lo g_{6} (\frac{k ^{2} - 36}{k - 6})

Simplify

\frac{k ^{2} - 36}{k - 6} : k + 6

= lo g_{6} (k + 6)

lo g_{10} (7) - 2 lo g_{10} (12)

ln (\frac{- y}{x y - 2})

lo g_{7} (\frac{7 x ^{9}}{y})

lo g_{4} (8) + 2 lo g_{4} (3)

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

What is log_{6}(k^2-36)-log_{6}(k-6) ?
The solution to log_{6}(k^2-36)-log_{6}(k-6) is log_{6}(k+6)