What is expand log_{b}(4x^2y) ?

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

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expand log_{b}(4x^2y)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{b} (x^{2}) = 2 lo g_{b} (x)

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

lo g_{b} (4) = 2 lo g_{b} (2)

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

- lo g_{10} (3 \cdot 1 0^{- 8})

lo g_{8} (5) + lo g_{8} (7)

lo g_{b} (b) - \frac{1}{3} lo g_{b} (y) + \frac{1}{4} lo g_{b} (z)

ln^{2} (3 x)

lo g_{10} (x^{2} - 9) - lo g_{10} (x^{2} + 7 x + 12)

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