What is expand log_{10}((x^5sqrt(y))/(z^2)) ?

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

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expand log_{10}((x^5sqrt(y))/(z^2))

expand

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

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

Solution steps

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

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

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

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

- ln (2 x) + ln (x)

ln (\frac{99}{49})

ln (\frac{4 x - 2}{3 x - 1})

ln (\frac{x + a}{x ^{2} + a ^{2}})

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

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