What is log_{3}(v)-4log_{3}(w) ?

The solution to log_{3}(v)-4log_{3}(w) is log_{3}(v/(w^4))

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simplify log_{3}(v)-4log_{3}(w)

simplify

lo g_{3} (v) - 4 lo g_{3} (w)

lo g_{3} (\frac{v}{w ^{4}})

Solution steps

lo g_{3} (v) - 4 lo g_{3} (w)

Apply log rule:

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

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

= lo g_{3} (v) - lo g_{3} (w^{4})

Apply log rule:

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

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

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

\frac{1}{2} lo g_{10} (x) + lo g_{10} (y) - 4 lo g_{10} (z)

4 lo g_{10} (2) - 2 lo g_{10} (3) - lo g_{10} (4)

ln (8) - ln (6)

ln (8) + ln (x)

lo g_{2} (a) + lo g_{2} (25) - lo g_{4} ((5 a)^{2})

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