What is log_{2}(x-6)+log_{2}(x-4)-log_{2}(x) ?

The solution to log_{2}(x-6)+log_{2}(x-4)-log_{2}(x) is log_{2}(((x-6)(x-4))/x)

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simplify log_{2}(x-6)+log_{2}(x-4)-log_{2}(x)

simplify

lo g_{2} (x - 6) + lo g_{2} (x - 4) - lo g_{2} (x)

lo g_{2} (\frac{( x - 6 ) ( x - 4 )}{x})

Solution steps

lo g_{2} (x - 6) + lo g_{2} (x - 4) - lo g_{2} (x)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (x - 6) + lo g_{2} (x - 4) = lo g_{2} ((x - 6) (x - 4))

= lo g_{2} ((x - 6) (x - 4)) - lo g_{2} (x)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{2} ((x - 6) (x - 4)) - lo g_{2} (x) = lo g_{2} (\frac{( x - 6 ) ( x - 4 )}{x})

= lo g_{2} (\frac{( x - 6 ) ( x - 4 )}{x})

ln (\frac{y}{x} + 4) - 6 ln (\frac{y}{x} - 1)

\frac{60}{2.2} ln (\frac{0.116}{0.039})

ln (\frac{3 x + 5}{2 x + 1})

lo g_{e} (\frac{x ^{3} - 3 x + 9}{x ^{3}})

- lo g_{10} (4.29 \cdot 1 0^{- 6})

What is log_{2}(x-6)+log_{2}(x-4)-log_{2}(x) ?
The solution to log_{2}(x-6)+log_{2}(x-4)-log_{2}(x) is log_{2}(((x-6)(x-4))/x)