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

The solution to expand log_{10}(z^3sqrt(x^5y)) is 3log_{10}(z)+log_{10}(sqrt(x)sqrt(y)sqrt(x^4))

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

expand

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

3 lo g_{10} (z) + lo g_{10} (x y x^{4})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x^{5} y = x y x^{4}

= 3 lo g_{10} (z) + lo g_{10} (x y x^{4})

\frac{1}{2} (lo g_{7} (r - 2) - lo g_{7} (r))

lo g_{b} (x^{2}) y

lo g_{4} (5) + lo g_{4} (9)

10 lo g_{10} (5 x)

lo g_{4} (\frac{3 x - 5}{x})

What is expand log_{10}(z^3sqrt(x^5y)) ?
The solution to expand log_{10}(z^3sqrt(x^5y)) is 3log_{10}(z)+log_{10}(sqrt(x)sqrt(y)sqrt(x^4))