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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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^{2} y)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- (2 lo g_{10} (z) + lo g_{10} (y)) : - 2 lo g_{10} (z) - lo g_{10} (y)

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

ln (w) + 3 ln (4 z)

lo g_{a} (\frac{x ^{2} y}{z})

ln (10 e)

lo g_{10} (\frac{7 z}{9})

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