What is log_{2}(k^2-4)-log_{2}(k-2) ?

The solution to log_{2}(k^2-4)-log_{2}(k-2) is log_{2}(k+2)

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simplify log_{2}(k^2-4)-log_{2}(k-2)

simplify

lo g_{2} (k^{2} - 4) - lo g_{2} (k - 2)

lo g_{2} (k + 2)

Solution steps

lo g_{2} (k^{2} - 4) - lo g_{2} (k - 2)

Apply log rule:

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

lo g_{2} (k^{2} - 4) - lo g_{2} (k - 2) = lo g_{2} (\frac{k ^{2} - 4}{k - 2})

= lo g_{2} (\frac{k ^{2} - 4}{k - 2})

Simplify

\frac{k ^{2} - 4}{k - 2} : k + 2

= lo g_{2} (k + 2)

lo g_{10} (9) + 3 lo g_{10} (2) - lo g_{10} (3)

5 lo g_{10} (x^{3} y) - 3 lo g_{10} (x y^{2})

ln (\frac{10}{100})

lo g_{10} (a) + lo g_{10} (b) - 2 lo g_{10} (c)

lo g_{4} (\frac{16}{x ^{4}})

What is log_{2}(k^2-4)-log_{2}(k-2) ?
The solution to log_{2}(k^2-4)-log_{2}(k-2) is log_{2}(k+2)