What is expand log_{4}((xy^2)^2) ?

The solution to expand log_{4}((xy^2)^2) is 2log_{4}(x)+4log_{4}(y)

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expand log_{4}((xy^2)^2)

expand

lo g_{4} ((x y^{2})^{2})

2 lo g_{4} (x) + 4 lo g_{4} (y)

Solution steps

lo g_{4} ((x y^{2})^{2})

Apply log rule:

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

lo g_{4} ((x y^{2})^{2}) = 2 lo g_{4} (x y^{2})

= 2 lo g_{4} (x y^{2})

Apply log rule:

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

2 lo g_{4} (x y^{2}) = 2 lo g_{4} (x) + 2 lo g_{4} (y^{2})

= 2 lo g_{4} (x) + 2 lo g_{4} (y^{2})

Apply log rule:

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

lo g_{4} (y^{2}) = 2 lo g_{4} (y)

= 2 lo g_{4} (x) + 2 \cdot 2 lo g_{4} (y)

Multiply the numbers:

2 \cdot 2 = 4

= 2 lo g_{4} (x) + 4 lo g_{4} (y)

2 lo g_{6} (y) - \frac{1}{2} lo g_{6} (x) + 4 lo g_{6} (w)

lo g_{6} (\frac{( x + 3 ) ^{2}}{3 y ^{3}})

2000 [ln (5) - ln (4)]

\frac{1}{3} ln (x) - 7 ln (y) + \frac{ln ( z )}{2}

What is expand log_{4}((xy^2)^2) ?
The solution to expand log_{4}((xy^2)^2) is 2log_{4}(x)+4log_{4}(y)