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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

ln (x) - ln (x - 5000)

ln (8) + 4 ln (4)

ln (\frac{y}{y - 2})

ln (5) + ln (x) - ln (y)

ln (\frac{x + 1}{x y})

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