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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

ln (x y) - ln (y)

ln (\frac{z}{x ^{5} y})

ln (8) + 3 ln (3)

ln (5.6 \cdot 7.8)

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