What is expand log_{10}((uv^6)^4) ?

The solution to expand log_{10}((uv^6)^4) is 4log_{10}(u)+24log_{10}(v)

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expand log_{10}((uv^6)^4)

expand

lo g_{10} ((u v^{6})^{4})

4 lo g_{10} (u) + 24 lo g_{10} (v)

Solution steps

lo g_{10} ((u v^{6})^{4})

Apply log rule:

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

lo g_{10} ((u v^{6})^{4}) = 4 lo g_{10} (u v^{6})

= 4 lo g_{10} (u v^{6})

Apply log rule:

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

4 lo g_{10} (u v^{6}) = 4 lo g_{10} (u) + 4 lo g_{10} (v^{6})

= 4 lo g_{10} (u) + 4 lo g_{10} (v^{6})

Apply log rule:

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

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

= 4 lo g_{10} (u) + 4 \cdot 6 lo g_{10} (v)

Multiply the numbers:

4 \cdot 6 = 24

= 4 lo g_{10} (u) + 24 lo g_{10} (v)

ln (\frac{197}{760})

ln (\frac{e ^{2 x} ( x + 4 ) ^{2}}{2 x + 1})

lo g_{9} (81 x^{8})

lo g_{5} (\frac{125}{x + 7})

What is expand log_{10}((uv^6)^4) ?
The solution to expand log_{10}((uv^6)^4) is 4log_{10}(u)+24log_{10}(v)