What is expand log_{6}((uv^3)^2) ?

The solution to expand log_{6}((uv^3)^2) is 2log_{6}(u)+6log_{6}(v)

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expand log_{6}((uv^3)^2)

expand

lo g_{6} ((u v^{3})^{2})

2 lo g_{6} (u) + 6 lo g_{6} (v)

Solution steps

lo g_{6} ((u v^{3})^{2})

Apply log rule:

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

lo g_{6} ((u v^{3})^{2}) = 2 lo g_{6} (u v^{3})

= 2 lo g_{6} (u v^{3})

Apply log rule:

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

2 lo g_{6} (u v^{3}) = 2 lo g_{6} (u) + 2 lo g_{6} (v^{3})

= 2 lo g_{6} (u) + 2 lo g_{6} (v^{3})

Apply log rule:

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

lo g_{6} (v^{3}) = 3 lo g_{6} (v)

= 2 lo g_{6} (u) + 2 \cdot 3 lo g_{6} (v)

Multiply the numbers:

2 \cdot 3 = 6

= 2 lo g_{6} (u) + 6 lo g_{6} (v)

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What is expand log_{6}((uv^3)^2) ?
The solution to expand log_{6}((uv^3)^2) is 2log_{6}(u)+6log_{6}(v)