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

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

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expand log_{10}(xyz^2)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (z^{2}) = 2 lo g_{10} (z)

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

lo g_{b} (u^{2} v)

lo g_{a} (u^{2} v^{3})

4 ln (x) - 4 ln (y)

lo g_{5} (x) - lo g_{5} (x^{4})

- 0.55 lo g_{2} (0.55) - 0.45 lo g_{2} (0.45)

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