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

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

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

simplify

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

3 lo g_{3} (x + 3) lo g_{3} (\frac{w}{y ^{4}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{3} (w) - lo g_{3} (y^{4}) = lo g_{3} (\frac{w}{y ^{4}})

= 3 lo g_{3} (x + 3) lo g_{3} (\frac{w}{y ^{4}})

ln (a) - ln (c)

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

10 lo g_{10} (- 200 x)

- lo g_{10} (8.5 \cdot 1 0^{- 6})

2.4 ln (3) + ln (2)

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