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

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

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

expand

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

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})

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} (z y^{4})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- (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_{3} (\frac{x}{x ^{2}})

lo g_{3} (7 x) - lo g_{3} (7 y)

lo g_{10} (\frac{8 c}{10})

lo g_{10} (0.5) + lo g_{10} (\frac{1}{2})

lo g_{9} (\frac{11}{17}) + lo g_{9} (\frac{17}{11})

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