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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} ((y - 1)^{3}) = 3 lo g_{10} (y - 1)

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- 0.66 \cdot lo g_{2} (0.66) - 0.33 lo g_{2} (0.33)

4 lo g_{3} (x) - 2 lo g_{3} (y)

lo g_{2} (4 x)

ln (96) - ln (6)

ln (- 2 e^{i z})

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