What is expand log_{3}(6xy^2) ?

The solution to expand log_{3}(6xy^2) is log_{3}(6)+log_{3}(x)+2log_{3}(y)

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expand log_{3}(6xy^2)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{3} (y^{2}) = 2 lo g_{3} (y)

= lo g_{3} (6) + lo g_{3} (x) + 2 lo g_{3} (y)

2000 (ln (140000) - ln (77000)) - 294

\frac{1}{2} ln (2 x) + \frac{5}{4} ln (4 x - 4) - \frac{3}{4} ln (4 x - 4)

ln (\frac{x ^{2} - 3 x}{x ^{2}})

2 ln (7) + 5 ln (y)

ln^{2} (x) + ln (x) + 1

What is expand log_{3}(6xy^2) ?
The solution to expand log_{3}(6xy^2) is log_{3}(6)+log_{3}(x)+2log_{3}(y)