What is expand log_{10}((x^3(x+1))/((x-2)^2)) ?

The solution to expand log_{10}((x^3(x+1))/((x-2)^2)) is 3log_{10}(x)+log_{10}(x+1)-2log_{10}(x-2)

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expand log_{10}((x^3(x+1))/((x-2)^2))

expand

lo g_{10} (\frac{x ^{3} ( x + 1 )}{( x - 2 ) ^{2}})

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

Solution steps

lo g_{10} (\frac{x ^{3} ( x + 1 )}{( x - 2 ) ^{2}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3} ( x + 1 )}{( x - 2 ) ^{2}}) = lo g_{10} (x^{3} (x + 1)) - lo g_{10} ((x - 2)^{2})

= lo g_{10} (x^{3} (x + 1)) - lo g_{10} ((x - 2)^{2})

Apply log rule:

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

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

= lo g_{10} (x^{3} (x + 1)) - 2 lo g_{10} (x - 2)

Apply log rule:

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

lo g_{10} (x^{3} (x + 1)) = lo g_{10} (x^{3}) + lo g_{10} (x + 1)

= lo g_{10} (x^{3}) + lo g_{10} (x + 1) - 2 lo g_{10} (x - 2)

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) + lo g_{10} (x + 1) - 2 lo g_{10} (x - 2)

lo g_{5} (x - 3) + lo g_{5} (3 x + 1)

lo g_{10} (25) + lo g_{10} (2) - lo g_{10} (3)

lo g_{6} (\frac{5 x ^{3}}{y})

ln (\frac{4}{17})

lo g_{4} (\frac{x ^{3}}{1024 y ^{5}})

What is expand log_{10}((x^3(x+1))/((x-2)^2)) ?
The solution to expand log_{10}((x^3(x+1))/((x-2)^2)) is 3log_{10}(x)+log_{10}(x+1)-2log_{10}(x-2)