What is expand log_{4}(16xy^3) ?

The solution to expand log_{4}(16xy^3) is 2+log_{4}(x)+3log_{4}(y)

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expand log_{4}(16xy^3)

expand

lo g_{4} (16 x y^{3})

2 + lo g_{4} (x) + 3 lo g_{4} (y)

Solution steps

lo g_{4} (16 x y^{3})

Apply log rule:

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

lo g_{4} (16 x y^{3}) = lo g_{4} (16) + lo g_{4} (x) + lo g_{4} (y^{3})

= lo g_{4} (16) + lo g_{4} (x) + lo g_{4} (y^{3})

Apply log rule:

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

lo g_{4} (y^{3}) = 3 lo g_{4} (y)

= lo g_{4} (16) + lo g_{4} (x) + 3 lo g_{4} (y)

lo g_{4} (16) = 2

= 2 + lo g_{4} (x) + 3 lo g_{4} (y)

3 ln (2) + 2 ln (3)

lo g_{10} (\frac{x}{4})

- 0.65 lo g_{2} (0.65) - 0.35 lo g_{2} (0.35)

lo g_{3} (9 x^{9}) - 2

ln (13 e)

What is expand log_{4}(16xy^3) ?
The solution to expand log_{4}(16xy^3) is 2+log_{4}(x)+3log_{4}(y)