What is expand log_{10}((5xy^2)/(z^3)) ?

The solution to expand log_{10}((5xy^2)/(z^3)) is log_{10}(5)+log_{10}(x)+2log_{10}(y)-3log_{10}(z)

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expand log_{10}((5xy^2)/(z^3))

expand

lo g_{10} (\frac{5 x y ^{2}}{z ^{3}})

lo g_{10} (5) + lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{5 x y ^{2}}{z ^{3}})

Apply log rule:

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

lo g_{10} (\frac{5 x y ^{2}}{z ^{3}}) = lo g_{10} (5 x y^{2}) - lo g_{10} (z^{3})

= lo g_{10} (5 x y^{2}) - lo g_{10} (z^{3})

Apply log rule:

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

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

= lo g_{10} (5 x y^{2}) - 3 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (5 x y^{2}) = lo g_{10} (5) + lo g_{10} (x) + lo g_{10} (y^{2})

= lo g_{10} (5) + lo g_{10} (x) + lo g_{10} (y^{2}) - 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (5) + lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (z)

ln (\frac{6.1 \cdot 7.36}{9.42 \cdot 1 0 ^{- 3}})

4 lo g_{10} (x) + 2 lo g_{10} (x - 1)

\frac{5 ln ( - 1 )}{6} - 3 \frac{1}{3}

\frac{1}{5} (6 ln (5) - ln (2))

ln (8) + ln (25)

What is expand log_{10}((5xy^2)/(z^3)) ?
The solution to expand log_{10}((5xy^2)/(z^3)) is log_{10}(5)+log_{10}(x)+2log_{10}(y)-3log_{10}(z)