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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{16} ln (\frac{1}{4})

lo g_{2} (5 lo g_{5} (π lo g_{π} (4)))

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

ln (\frac{5 x ^{2}}{8 - x})

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