What is expand log_{10}(w^6sqrt(u*v)) ?

The solution to expand log_{10}(w^6sqrt(u*v)) is 6log_{10}(w)+log_{10}(sqrt(uv))

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expand log_{10}(w^6sqrt(u*v))

expand

lo g_{10} (w^{6} u \cdot v)

6 lo g_{10} (w) + lo g_{10} (uv)

Solution steps

lo g_{10} (w^{6} uv)

Apply log rule:

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

lo g_{10} (w^{6} uv) = lo g_{10} (w^{6}) + lo g_{10} (uv)

= lo g_{10} (w^{6}) + lo g_{10} (uv)

Apply log rule:

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

lo g_{10} (w^{6}) = 6 lo g_{10} (w)

= 6 lo g_{10} (w) + lo g_{10} (uv)

2 ln (a) - ln (b)

lo g_{10} (500) - lo g_{10} (2)

lo g_{4} (x^{2} - 16) - lo g_{4} (x) - lo g_{4} (x - 4)

lo g_{b} (x^{7} z)

lo g_{a} (\frac{x ^{4}}{y z ^{5}})

What is expand log_{10}(w^6sqrt(u*v)) ?
The solution to expand log_{10}(w^6sqrt(u*v)) is 6log_{10}(w)+log_{10}(sqrt(uv))