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

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

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

expand

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

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

Solution steps

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

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

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

lo g_{5} (\frac{1}{x})

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

4 ln (x) + 6 ln (x^{\frac{1}{3}})

lo g_{2} (\frac{3 x ^{2}}{( x - 1 ) ^{2}})

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

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