What is 2log_{3}(x)+4log_{3}(x-1)+log_{3}(y) ?

The solution to 2log_{3}(x)+4log_{3}(x-1)+log_{3}(y) is log_{3}(x^2(x-1)^4y)

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simplify 2log_{3}(x)+4log_{3}(x-1)+log_{3}(y)

simplify

2 lo g_{3} (x) + 4 lo g_{3} (x - 1) + lo g_{3} (y)

lo g_{3} (x^{2} (x - 1)^{4} y)

Solution steps

2 lo g_{3} (x) + 4 lo g_{3} (x - 1) + lo g_{3} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{3} (x^{2}) + 4 lo g_{3} (x - 1) + lo g_{3} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{3} (x - 1) = lo g_{3} ((x - 1)^{4})

= lo g_{3} (x^{2}) + lo g_{3} ((x - 1)^{4}) + lo g_{3} (y)

Apply log rule:

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

lo g_{3} (x^{2}) + lo g_{3} ((x - 1)^{4}) = lo g_{3} (x^{2} (x - 1)^{4})

= lo g_{3} (x^{2} (x - 1)^{4}) + lo g_{3} (y)

Apply log rule:

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

lo g_{3} (x^{2} (x - 1)^{4}) + lo g_{3} (y) = lo g_{3} (x^{2} y (x - 1)^{4})

= lo g_{3} (x^{2} (x - 1)^{4} y)

- lo g_{10} (8.4 \cdot 1 0^{- 4})

lo g_{10} (\frac{x ^{2} y ^{18}}{z ^{8}})

ln (\frac{r}{2 s})

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

lo g_{10} ((m^{n}) \cdot (p^{q}))

What is 2log_{3}(x)+4log_{3}(x-1)+log_{3}(y) ?
The solution to 2log_{3}(x)+4log_{3}(x-1)+log_{3}(y) is log_{3}(x^2(x-1)^4y)