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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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