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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{x}{w})

ln (1 \cdot 1 0^{- 3})

ln (100) - ln (101)

ln (e^{3})

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