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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

\frac{1}{2} lo g_{3} (x - 3) + 6 lo g_{3} (y)

lo g_{3} (4) + lo g_{3} (7)

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

ln (\frac{53}{7})

ln (11) - 3 ln (2)

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