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

The solution to log_{3}(x)+4log_{3}(y) is log_{3}(xy^4)

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

simplify

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

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

Solution steps

lo g_{3} (x) + 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})

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

Apply log rule:

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

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

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

\frac{1}{3} ln ∣ y - 1 ∣ - \frac{1}{3} ln ∣ y + 2 ∣

ln (20) + 2 ln (\frac{1}{2}) + \frac{1}{3} ln (27)

3.3 ln (6) - 7.2 ln (2) - 0.9 ln (2)

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

- 3 ln (x) - 3 ln (y) + 3 ln (z)

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