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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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

2 ln (2) + 2 ln (x) - ln (y)

\frac{1}{2} ln (u^{2} + 1) + ln (u + 1)

ln (\frac{1.5 \cdot 1 0 ^{5}}{1.5 \cdot 1 0 ^{10}})

lo g_{10} (1024) - 3 lo g_{10} (2) - lo g_{10} (3)

lo g_{10} (t^{3})

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