What is 2log_{10}(x)-log_{10}(x-1) ?

The solution to 2log_{10}(x)-log_{10}(x-1) is log_{10}((x^2)/(x-1))

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simplify 2log_{10}(x)-log_{10}(x-1)

simplify

2 lo g_{10} (x) - lo g_{10} (x - 1)

lo g_{10} (\frac{x ^{2}}{x - 1})

Solution steps

2 lo g_{10} (x) - lo g_{10} (x - 1)

Apply log rule:

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

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

= lo g_{10} (x^{2}) - lo g_{10} (x - 1)

Apply log rule:

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

lo g_{10} (x^{2}) - lo g_{10} (x - 1) = lo g_{10} (\frac{x ^{2}}{x - 1})

= lo g_{10} (\frac{x ^{2}}{x - 1})

- lo g_{10} (6.8 \cdot 1 0^{- 4})

ln (\frac{x}{e ^{6 x}})

lo g_{10} (1 y)

ln (\frac{x x + 1}{x ^{2} + 1})

lo g_{10} (3 b)

What is 2log_{10}(x)-log_{10}(x-1) ?
The solution to 2log_{10}(x)-log_{10}(x-1) is log_{10}((x^2)/(x-1))