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

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

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expand log_{b}((xy)^3)

expand

lo g_{b} ((x y)^{3})

3 lo g_{b} (x) + 3 lo g_{b} (y)

Solution steps

lo g_{b} ((x y)^{3})

Apply log rule:

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

lo g_{b} ((x y)^{3}) = 3 lo g_{b} (x y)

= 3 lo g_{b} (x y)

Apply log rule:

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

3 lo g_{b} (x y) = 3 lo g_{b} (x) + 3 lo g_{b} (y)

= 3 lo g_{b} (x) + 3 lo g_{b} (y)

4 lo g_{10} (a) + lo g_{10} (b)

ln (\frac{5 \cdot 8 ^{5}}{2.9})

ln (8 e^{- 300 t})

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ln (200) - ln (100)

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