What is log_{10}((4x^3)/(y^2)) ?

The solution to log_{10}((4x^3)/(y^2)) is 2log_{10}(2)+3log_{10}(x)-2log_{10}(y)

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simplify log_{10}((4x^3)/(y^2))

simplify

lo g_{10} (\frac{4 x ^{3}}{y ^{2}})

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

Solution steps

lo g_{10} (\frac{4 x ^{3}}{y ^{2}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{4 x ^{3}}{y ^{2}}) = lo g_{10} (4 x^{3}) - lo g_{10} (y^{2})

= lo g_{10} (4 x^{3}) - lo g_{10} (y^{2})

lo g_{10} (4 x^{3}) = 2 lo g_{10} (2) + 3 lo g_{10} (x)

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

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

lo g_{3} (20) - lo g_{3} (4)

ln (\frac{11}{16})

ln (\frac{3}{4}) - 1

ln (e^{3} \cdot (e^{2} - 1))

lo g_{b} (\frac{m}{n})

What is log_{10}((4x^3)/(y^2)) ?
The solution to log_{10}((4x^3)/(y^2)) is 2log_{10}(2)+3log_{10}(x)-2log_{10}(y)