What is expand log_{10}(x^2y^5z) ?

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

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expand log_{10}(x^2y^5z)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

= 2 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)

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

ln (2 e^{- x^{2}} x^{2})

ln (7) + 4 ln (4)

- lo g_{10} (6.3 \cdot 1 0^{- 9})

6 ln (c) + 6 ln (x)

\frac{π}{8} lo g_{10} (2)

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