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

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

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

simplify

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

3 lo g_{10} (x) - lo g_{10} (z) - 4 lo g_{10} (y)

Solution steps

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

Apply log rule:

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

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

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

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

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

= 3 lo g_{10} (x) - (lo g_{10} (z) + 4 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (z) + 4 lo g_{10} (y)) = - lo g_{10} (z) - 4 lo g_{10} (y)

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

lo g_{10} (30) + lo g_{10} (\frac{1}{10})

ln (14 x y)

6 x^{2} (x^{3} + 4) + ln (2 x) + 1

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

ln (\frac{3 \cdot x ^{4}}{y})

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