What is 2log_{3}(u)-log_{3}(v) ?

The solution to 2log_{3}(u)-log_{3}(v) is log_{3}((u^2)/v)

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simplify 2log_{3}(u)-log_{3}(v)

simplify

2 lo g_{3} (u) - lo g_{3} (v)

lo g_{3} (\frac{u ^{2}}{v})

Solution steps

2 lo g_{3} (u) - lo g_{3} (v)

Apply log rule:

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

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

= lo g_{3} (u^{2}) - lo g_{3} (v)

Apply log rule:

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

lo g_{3} (u^{2}) - lo g_{3} (v) = lo g_{3} (\frac{u ^{2}}{v})

= lo g_{3} (\frac{u ^{2}}{v})

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

2 ln (x) - 5 ln (y)

lo g_{2} (\frac{x ^{5} 4 ^{x}}{2 ^{x^{4}}})

6 lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{2} (x) - lo g_{2} (y) - 3 lo g_{2} (z)

What is 2log_{3}(u)-log_{3}(v) ?
The solution to 2log_{3}(u)-log_{3}(v) is log_{3}((u^2)/v)