What is 2log_{10}(x-2)-log_{10}(x) ?

The solution to 2log_{10}(x-2)-log_{10}(x) is log_{10}(((x-2)^2)/x)

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simplify 2log_{10}(x-2)-log_{10}(x)

simplify

2 lo g_{10} (x - 2) - lo g_{10} (x)

lo g_{10} (\frac{( x - 2 ) ^{2}}{x})

Solution steps

2 lo g_{10} (x - 2) - lo g_{10} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{10} (x - 2) = lo g_{10} ((x - 2)^{2})

= lo g_{10} ((x - 2)^{2}) - lo g_{10} (x)

Apply log rule:

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

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

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

lo g_{5} (x + y) - 2 lo g_{5} (x - y)

lo g_{3} (\frac{9}{x + 4})

5 lo g_{b} (x) - lo g_{b} (y)

- lo g_{10} (2.8 \cdot 1 0^{- 5})

0.9 ln (6) - 2.4 ln (8)

What is 2log_{10}(x-2)-log_{10}(x) ?
The solution to 2log_{10}(x-2)-log_{10}(x) is log_{10}(((x-2)^2)/x)