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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{5} (\frac{7 z}{6})

\frac{1}{2} lo g_{10} (5)

lo g_{5} ((x + 9) (x + 9))

lo g_{4} ((\frac{u}{v ^{6}})^{2})

lo g_{4} (2 x + 3) + lo g_{4} (2 x + 15)

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