What is expand log_{10}(z^5sqrt(x^3y)) ?

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

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expand log_{10}(z^5sqrt(x^3y))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (z^{5}) = 5 lo g_{10} (z)

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

x^{3} y = x y x^{2}

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

lo g_{10} (\frac{p q ^{3}}{s})

lo g_{10} (\frac{c ^{6}}{a b ^{3}})

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

lo g_{6} (\frac{36 a ^{6} 1 - b}{c ( b + 5 ) ^{2}})

ln (\frac{17}{16})

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