What is expand log_{10}(uv^4*w^4) ?

The solution to expand log_{10}(uv^4*w^4) is log_{10}(u)+4log_{10}(v)+4log_{10}(w)

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expand log_{10}(uv^4*w^4)

expand

lo g_{10} (u v^{4} \cdot w^{4})

lo g_{10} (u) + 4 lo g_{10} (v) + 4 lo g_{10} (w)

Solution steps

lo g_{10} (u v^{4} w^{4})

Apply log rule:

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

lo g_{10} (u v^{4} w^{4}) = lo g_{10} (u) + lo g_{10} (v^{4}) + lo g_{10} (w^{4})

= lo g_{10} (u) + lo g_{10} (v^{4}) + lo g_{10} (w^{4})

Apply log rule:

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

lo g_{10} (v^{4}) = 4 lo g_{10} (v)

= lo g_{10} (u) + 4 lo g_{10} (v) + lo g_{10} (w^{4})

Apply log rule:

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

lo g_{10} (w^{4}) = 4 lo g_{10} (w)

= lo g_{10} (u) + 4 lo g_{10} (v) + 4 lo g_{10} (w)

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

9 lo g_{10} (x) - 4 lo g_{10} (y)

ln (\frac{7 x}{x - 7})

lo g_{10} (35.89) - lo g_{10} (24.33)

\frac{1}{2} ln (5) - \frac{1}{2} ln (4)

What is expand log_{10}(uv^4*w^4) ?
The solution to expand log_{10}(uv^4*w^4) is log_{10}(u)+4log_{10}(v)+4log_{10}(w)