What is expand log_{6}((u^2v)^4) ?

The solution to expand log_{6}((u^2v)^4) is 8log_{6}(u)+4log_{6}(v)

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expand log_{6}((u^2v)^4)

expand

lo g_{6} ((u^{2} v)^{4})

8 lo g_{6} (u) + 4 lo g_{6} (v)

Solution steps

lo g_{6} ((u^{2} v)^{4})

Apply log rule:

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

lo g_{6} ((u^{2} v)^{4}) = 4 lo g_{6} (u^{2} v)

= 4 lo g_{6} (u^{2} v)

Apply log rule:

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

4 lo g_{6} (u^{2} v) = 4 lo g_{6} (u^{2}) + 4 lo g_{6} (v)

= 4 lo g_{6} (u^{2}) + 4 lo g_{6} (v)

Apply log rule:

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

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

= 4 \cdot 2 lo g_{6} (u) + 4 lo g_{6} (v)

Multiply the numbers:

4 \cdot 2 = 8

= 8 lo g_{6} (u) + 4 lo g_{6} (v)

lo g_{6} (18 x)

ln (\frac{e ^{4}}{13})

lo g_{5} (a^{4} b^{2})

\frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( 7 ) - 2 ln ( 2 )}

5 lo g_{2} (m) + 4 lo g_{2} (n)

What is expand log_{6}((u^2v)^4) ?
The solution to expand log_{6}((u^2v)^4) is 8log_{6}(u)+4log_{6}(v)